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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.
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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.
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Answer:
Squaring and subtracting (2) from (1)
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Question (7):
Eliminate q between the equation 
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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.
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Answer:
Squaring and adding,
 
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Question (9):
Eliminate q between x = sin q + cos q, y = tan q + cot q.
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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).
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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)
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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).
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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.
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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.
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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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