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Question
If A and B are complementary angles, prove that:
cot A cot B – sin A cos B – cos A sin B = 0
Solution
Since, A and B are complementary angles, A + B = 90°
cot A cot B – sin A cos B – cos A sin B
= cot A cot (90° – A) – sin A cos (90° – A) – cos A sin (90° – A)
= cot A tan A – sin A sin A – cos A cos A
= 1 – (sin2 A + cos2 A)
= 1 – 1
= 0
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