Question

If A and B are the acute angles of a right angled triangle ABC,right angled at C .Prove that:1 + cot2A = sec2B ​

Answer 1

GIVEN

A and B are acute angles of a right angle triangle ABC. So

$A+B+ \frac{π}{2}= π$

$A+B= \frac{π}{2}$

PROOF

LHS

$=1+cot²(A)$

$=1+cot²(\frac{π}{2}-B)$

$=1+tan²(B)$

$=sec²(B)$

= RHS

Hence Proved

Answer 2

Answer:

sec^2B

I HOPE THIS WILL HELP YOU...........