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Question (1):
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Answer:



 Solve the equations sec q + tan q = x ....(1)





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Question (2):
If 3 sinq + 5 cosq = 5, show that 5 sinq - 3 cosq = 3. |
Answer:





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Question (3):
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Answer:



 Or

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Question (4):
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Answer:
 In the figure


 
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Question (5):
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Answer:
 In the figure


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Question (6):
Eliminate q between the equation x = a sec q and y = b tan q. |
Answer:

 Squaring and subtracting (2) from (1)

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Question (7):
Eliminate q between the equation  |
Answer:






 Squaring and adding,



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Question (8):
If a sec q - x tan q = y, b sec q + y tan q = x, eliminate q. |
Answer:

 Squaring and adding,



 
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Question (9):
Eliminate q between x = sin q + cos q, y = tan q + cot q. |
Answer:





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Question (10):
Find sin q if


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Answer:
 (i) In I quadrant sin q is positive
 (ii) In IV quadrant sin q is negative.
 (iii) In III quadrant sin q is negative.
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Question (11):
Find cos q if


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Answer:







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Question (12):
 (i) sin (x + y) (ii) sin (x - y) (iii) cos (x + y) (iv) cos (x - y). |
Answer:






 (ii) sin (x - y) = sin x cos y - cos x sin y

 (iii) cos (x + y) = cos x cos y - sin x sin y

 (iv) cos (x - y) = cos x cos y + sin x sin y

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Question (13):
 (i) cos (x - y) (ii) sin (x + y) |
Answer:
 Both sin x and cos x are positive as x lies in I quadrant.
 Both cos y and sin y are positive as y lies in I quadrant. i) cos (x - y) = cos x cos y + sin x sin y

 ii) sin (x + y) = sin x cos y + cos x sin y

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Question (14):
Find x, if



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Answer:
  cos x is negative in both II and III quadrants.




cos x lies in III quadrant only.

  positive in I and IV quadrants.
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Question (15):
 (i) cos (a + b) (ii) sin (a - b) (iii) sin (a + b) (iv)cos (a - b). |
Answer:






 (i) cos (a + b) = coa a cos b - sin a sin b

 ii) sin (a - b) = sin a cos b - cos a sin b


 iii) sin (a + b) = sin a cos b + cos a sin b

 iv) cos(a - b) = cos a cos b + sin a sin b

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Question (16):

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Answer:










 sin(q+f) = sinq cosf + cosq sinf

 Since sin (q + f) and cos (q + f) are both positive, (q + f) lies in the I quadrant. |
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Question (17):
in the first quadrant. Find sin A. |
Answer:










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Question (18):
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Answer:

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Question (19):
Prove that
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Answer:



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Question (20):
Prove that

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Answer:











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Question (21):
Prove that
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Answer:


 = (1 - sin2q) - sin2q
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Question (22):
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Answer:
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Question (23):
Prove that
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Answer:
 = cosq + 1



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Question (24):
Prove that
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Answer:
LHS = 1 + sin A


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Question (25):
Prove that cos4A = 8cos4A - 8cos2A + 1. |
Answer:
LHS = cos2 2A - sin2 2A




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Question (26):
Prove that
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Answer:
 LHS = cos x cos y + sin x sin y


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Question (27):
Prove that
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Answer:
 

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Question (28):
Prove that
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Answer:



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Question (29):
Prove that
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Answer:






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Question (30):
Prove that
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Answer:







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