Question

If secA = 5/4 prove that cos²A = 1- sin²A

Answer 1

Hi there !!

It is given that secA= 5/4

We know that secA is reciprocal of cosA

So, we can say that cosA =4/5

Consider ∆PBC,By Pythagoras theorem,

PC²= PB²+BC²

5k²=4k²+BC²

BC²= 9k² = BC= 3

SinA = P/H = 3/5

Now,

cos²A = 1- sin²A

(4/5)²= 1- (3/5)²

16/25 = 1-9/25

16/25= 16/25

Hence proved

Thankyou :)