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Question 102
If A and B are complementary angles, then the value of $$sin A cos B + cos A sin B tan A tan B + sec^2 A - cot^2 B$$ is
Solution
B = 90-A (Since the angles are complementary.
$$Cos B = Cos (90-A) = Sin A$$
$$Sin B =Sin (90-A) = Cos B$$
$$tan B = tan(90-A) = Cot A$$
$$Cot ^{2}B = Cot^{2} (90-A) = Tan^{2}A$$
$$sin A cos B + cos A sin B tan A tan B + sec^2 A - cot^2 B = sin^{2}A + cos^{2} tan A cot A + sec^{2}A - tan^{2} A$$
$$= sin^{2} A + cos^{2} A +1$$
$$=1+1 =2$$
Option A is the correct answer.
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