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–
[ A ] 1
[ B ] -1
[ C ] 2
[ D ] 0
Answer : Option A
Explanation :
sin A cos B + cos A sin B – tan A tan B
+ $sec^2$ A – $cot^2$ B
= sinA sin A + cosA cosA – tanA. cot A
+ $sec^2$ A – $tan^2$ B
= ($sec^2$ A + $cot^2$ A) – 1 + (1)
= 1 – 1 + 1
= 1