If A + B = 90º, then the expression (cot A)/(cot B) + cos²A + cos²B is equal to:

If A + B = 90º, then the expression (cot A)/(cot B) +…

If A + B = 90º, then the expression $\frac{cot A}{cot B}$ + cos²A + cos²B is equal to:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. cosec²A.

Given that

If A + B = 90º

The value of $\frac{cot A}{cot B}$ + cos²A + cos²B

⇒ $\frac{cot A}{cot B}$ + cos²A + cos²B

⇒ $\frac{cot A}{cot (90^0 - A)}$ + cos²A + cos² (90 - A)

⇒ $\frac{cot A}{tan A}$ + cos²A + sin²A

⇒ cot² A + 1

⇒ cosec²A