help with trigonometric identities

Introduction - The trigonometric ratio's are: Sine, Cosine, Tangent, Cotangent, Secant, and Cosecan..

Some Trigonometrical Identities - 1. sin A = cos (90 o - A) 2. 3. tan A x tan (90 o - A) = 1 4. sin 2 A + cos 2 A = 1 5. 1 + tan 2 A = sec 2 A 6. 1 + cot 2 A = cosec 2 A Let us prove the above identities. Let D ABC be a right-angled triangle with B = 90 o . Let BC = a,..

1. sin A = cos (90 o - A). 2. sin A / cos a = tan A. 3. tan A x tan (90 o - A) = 1. 4. sin 2 A + cos 2 A = 1. 5. 1 + tan 2 A = sec 2 A. 6. 1 + cot 2 A = cosec 2 A. Where 'A' is the angl..

In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relationship exists among the angles considered. Many interestin..

When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference. (1) (2) (3) (4) (5) (7) (..

Summary - sin A = cos (90 o - A) tan A . tan (90 o - A) = 1 sin 2 A + cos 2 A = 1 1 + tan 2 A = sec 2 A 1 + cot 2 A = cosec 2..

- Identical properties of circular functions and trigonometric functions. Let O be the origin. Let OA be the unit radius of the circle drawn with O as centre. Let OA trace an angle when OA takes the position OP. Then The tracing of the angle q and the arc AP = P( q ) are one and..

Identical equations or Identities - Now study the equations given below: a) x + 3 + x + 4 = 2x + 7 2x + 7 = 2x + 7 (By simplification) [ \ any value given to 'x' always satisfies the equation] Similarly, b) (3a + 4) + 2 (a - 1) = 5a + 2 i.e., 5a + 2 = 5a + 2 (By simplification) ..

A trigonometric equation is an equation involving the trigonometric functions of unknown angles. Example; sin x = 1/..

Introduction - The t-ratios of acute angles are given in tables of natural sines, natural cosines and natural tangents. In this chapter, we will discuss (i) how to read trigonometric tables, (ii) how to find the angle when the value of a t-ratio is give..