Question

Verify the identity (simplify at each step)

8cot^2(y)(sec^2(y) - 1) = 8

Answer 1

see the procedure

Explanation:

we have

`8cot^(2)(y)(sec^(2)(y)-1)=8`

Remember that

`tan(y)=(sin(y))/(cos(y))`

`tan(y)=(1)/(cot(y))`

`sec(y)=(1)/(cos(y))`

`sin^2(y)+cos^2(y)=1` ----->
`sin^2(y)=1-cos^2(y)`

`(sec^(2)(y)-1)=(1)/(cos^2(y))-1=(1-cos^2(y))/(cos^2(y))=(sin^2(y))/(cos^2(y))=tan^2(y)=(1)/(cot^2(y))`

substitute

`8cot^(2)(y)((1)/(cot^2(y)))=8`

Simplify

`8=8` ----> is verified