Question

hiii ........plz solve it. if A+B = 90 then (1-sin^2A)(1+cot^2B)=?? ​

Answer 1

$\huge{\textbf{SOLUTION}}$

Given -

A+B = 90°

So,

=> (1-sin²A)(1+cot²B)

As we know,

$\boxed{1-sin^{2}A=cos^{2}A}$

$\boxed{1+cot^{2}A=cosec^{2}A}$

Substituting this, we get

cos²A × cosec²B

As we know,

$\boxed{cosec(90-\theta)=sec\theta}$

It's given that

A+B = 90

>> B = 90-A

Hence, we get

cos²A × cosec²B

=>cos²A × cosec²(90 - A)

=> cos²A×sec²A

=> cos²A × $\frac{1}{cos^{2}A}$

= 1

$\mathbb{HENCE}$

(1 - sin²A)(1+cot²B) = 1