SocialTwist Tell-a-Friend

Ask a Question? Get an Answer!


Question: The value of the expression 3 cosec 20° - sec 20° is equal to _______


A ) 4
B ) 2
C ) 2 sin 20°sin 40°
D ) 4 sin 20°sin 20°

Steps to derive

1 Given 3 cosec 20° - sec 20°

2 = 3sin 20° -1cos 20°
 [Use cosec θ = 1sin θ and sec θ = 1cos θ.]

3 = 3 cos 20° - sin 20°sin 20° cos 20°
 [Simplify.]

4 = 2[32 cos 20° -12sin 20°]22 sin 20° cos 20°
 [Multiply and divide the numerator and denominator by 2.]

5 = 4[32 cos 20° -12sin 20°]sin 40°
 [Use 2sin A cos A = sin 2A.]

6 = 4(sin 60° cos 20° - cos 60° sin 20°)sin 40°
 [Use 32 as sin 60° and 12as cos 60°.]

7 4 [sin (60° - 20°)]sin 40°
 [Use sin A cos B - cosA sin B = sin (A - B).]

8 4 (sin 40°)sin 40° = 4
 [Simplify.]

9 Therefore the value of the expression 3 cosec 20° - sec 20° is 4.



Hence the right answer is Option A

Click Here To Go Back


Few Other Questions -

  • Evaluate : ∫cos2 43x1-sin  43xdx..
  • Evaluate : ∫11+sin 5x dx..
  • Evaluate : ∫cosec 4xcosec 4x-cot 4x dx..
  • Three cyclists P, Q and R with the same speed starts from A to reach E as shown in the fig..
  • Evaluate : ∫sin2 7xsec2 7xdx..
  • Evaluate : ∫1+cos 6xdx, where x ∈ (0,π2)...
  • Evaluate : ∫1+cos 2xdx, where x ∈ (π2, π)...
  • Find the sum of oranges shown by the varieties Valencia and Tangerine, from the table...
  • Evaluate : ∫sin23x1+cos 3x dx..
  • Evaluate : ∫11-sin 4x dx..
  • Evaluate : ∫11+cos 2x dx..
  • Evaluate : ∫11-cos 2x dx..
  • Evaluate : ∫sec 2xsec 2x+tan 2x dx..
  • Evaluate : ∫cos25x.cosec25x dx..
  • Evaluate : ∫sec24x.cosec24xdx..
  • Evaluate : ∫cot- 11-cos 10x1+cos 10xdx..
  • Evaluate : ∫e-logecosec 7xdx..
  • Evaluate : ∫e2logecot 3xdx..
  • Evaluate : ∫42log4 sec 9xdx..
  • Evaluate : ∫e4loge xdx..
  • Evaluate : 17(∫8-log64x2dx)..
  • Evaluate : ∫a4x+10dx..
  • Evaluate : ∫e-loge sec 35xdx..
  • Evaluate : ∫eloge4(sec 12x)(tan 12x)dx..
  • Evaluate : ∫eloge42(cosec 4x)(cot 4x)dx..
  • Evaluate : ∫e- 5logex7dx..
  • Evaluate : ∫3-log27x3dx..
  • Evaluate : ∫75x+35dx..
  • Annie and her friends picked flowers from a garden. Name those Who have less than 15 flowe..
  • If f (x) = 7x - 2 and g [f (x)] = 3x2 - 70 then find g (33)...
  • If b = 15+256+15-256, then find b2...
  • Evaluate ∫1+sin2 5x1+cos 10x dx...
  • Evaluate ∫39sin 5x5+5sin 5x dx...
  • Evaluate ∫6cos3 7x+7sin3 7x8sin2 7xcos2 7x dx...
  • Evaluate ∫sin6x+cos6xsin2xcos2xdx...
  • Evaluate ∫42(sin 6x+cos 6x)1+sin 12x dx where x ∈ (0, π2)..
  • Evaluate ∫1+cos2 7x1-cos 14x dx ...
  • Evaluate ∫49cos 8x1-cos 8x dx...
  • Evaluate ∫3cos3 4x-4sin3 4x5sin2 4xcos2 4x dx...
  • Evaluate : ∫9x81+x18 dx..
  • Choose the figure that shows 12 apples if..
  • Evaluate : ∫1x2+14x+50dx..
  • Evaluate : ∫e8x1+e16xdx..
  • Choose the figure that shows less than 9 marbles if..
  • Find the slope of the line passing through the points A (7, 9) and B (9, 13)...
  • What is the slope of a line on which for every point the x coordinate is same?..
  • What is the slope of the line on which for every point the ordinate is same?..
  • The angle of inclination of a line is 3 π4. What is the slope of the line?..
  • If t > 1and m is the slope of the line joining the points (2t2 , 4t) and (2t2 , 4t), ..
  • Find the values of k such that the points (k + 2, 2), (2k + 2, 4) and (2k + 3, 2k + 1) are..
  • What is the equation of the line passing through the points (2, 5) and (5, 2)?..
  • What is the equation of the line passing through (- 3, - 7) with the slope 5?..
  • Find the equation of the line with slope 7 and y - intercept 11...
  • What is the equation of the line which has 7 and - 8 as the x, y - intercepts?..
  • What is the equation of the line passing through (6, 12) and has an angle of inclination 3..
  • What is the equation of a vertical line whose x - intercept is 3?..
  • What are the x and y - intercepts of the line 5x + 6y - 30 = 0?..
  • Find the slope and y - intercept of the line 11x - 10y + 20 = 0...
  • Write the equation of the line having slope 5 and x- intercept 4...
  • Find the equation of line passing through (10, 8) and parallel to line 8x + 9y - 46 = 0...
  • Write the equation of the line passing through (6, 3) and perpendicular to the line 5x + 6..
  • Evaluate ∫x7tan- 1(x8)1+x16dx...
  • The number of pencils Rose and her friends have is shown in the table. Find the number of ..
  • Choose the value of x2, if x represents the volume of the box shown and a = 196 in., b = 8..
  • Find the sum of the volumes of the 3 cubes shown if a = 4 m, b = 6 m and c = 8 m...
  • Find the surface area of the figure which is formed by joining 3 cubes as shown where, a ..
  • Find the slope of the line passing through the points A (3, 3) and B (6, 9)...
  • The angle of inclination of a line is 3 π4. What is the slope of the line?..
  • Find the angle of inclination of a line whose slope is -3...
  • If a ≠ - 5, then what is the slope of the line joining the points (- 10a, 25 ) , (a2 + ..
  • What is the slope of the line 6x + 13y + 27 = 0?..
  • Find the angle of inclination of the line x + y + 3 = 0...
  • What is the equation of the line passing through the points (4, 8) and (5, 5)?..
  • What is the equation of the line which has 3 and - 7 as the x, y - intercepts?..
  • What is the equation of the line passing through (6, 8) and has an angle of inclination 3&..
  • What are the x and y - intercepts of the line 5x + 3y - 45 = 0?..
  • Find the slope and y - intercept of the line 8x - 17y + 68 = 0...
  • Write the equation of the line having slope 5 and x - intercept 11...
  • Find the equation of line passing through (3, 4) and parallel to line x + 4y - 11 = 0...
  • Write the equation of the line passing through (4, 5) and perpendicular to the line 9x + 2..
  • Hanna and her friends are playing a game. The winner is the one who selects a thing which ..
  • Radius(r) of the inner most circle is 13 cm. Radius of the each consecutive circle increas..
  • Robert went to the playground with his son. A cycling race started from A, completed one r..
  • Find the sum of the solutions of the equation | 2x - 1 | = 9...
  • Find the number of solutions of the equation | 3x + 2 | = - 6...
  • The time period of a simple pendulum of length l ft is given by T = (0.8) 2l sec. Find the..
  • Find the area of the shaded portion. The two triangles are equilateral with sides 40 cm an..
  • Find the area of the shaded portion. The side of a regular hexagon is 16 cm and radius of ..
  • A plot of land as shown has to be levelled. If the rate of levelling is $28 per square met..
  • Find the area of the shaded region. [Take a = 2 m, c = 4 m, b = 8 m, d = 12 m, and π = ..
  • Find the sum of areas of the top and bottom faces of the figure which is formed by joinin..
  • A model of an arch as shown is to be constructed for testing in a wind tunnel. Find the to..
  • Cross section of an R.C.C beam is as shown. The smaller circles represent iron bars of dia..
  • A carpet has 15 special patterns as shown. The rate of making the pattern is $3 per square..
  • Find the ratio of the area of the shaded portion to that of the unshaded portion. [Take &p..
  • Lindsay takes out one pencil from a box containing 5 different colored pencils. Find the n..
  • Which of the following is true for the expression a3+b3+c3 - 3abc if a, b, c are distinct ..
  • The height of the Eiffel Tower located in Paris is 986 ft. Express the height in scientifi..
  • The height of the Sears Tower located in Chicago is 1,454 ft. Express the height in scient..
  • The height of the Petronas Twin Towers located in Malaysia is 1,483 ft. Express the height..
    		•