Verify the identity by converting the left side into sines and cosines. (Simplify at each step.

Question

5 cot²(y)(sec²(y) − 1) = 5

Answer 1

divide by 5 leaving

cot^2(y)(sec^2(y)-1)=1

if you dont know what to do, convert everything into sines and cosines

cos^2(y)/sin^2(y) x (1/cos^2(y)-1)=1

1/sin^2(y) -cos^2(y)/sin^2(y)= 1

(1-cos^2(y))/sin^2(y)= 1

sin^2(y)/sin^2(y)=1

1=1

qed

Answer 2

I solved it step by step, explaining along the way.

Full solution provided.

Answer 3

sec² y = 1 + cot² y, This is a Pythagorean Identity. Learn it.

Now substitute and simplify.