Question

Can someone tell me if this is an identity or not?

Answer 1

To start you want to expand the first term.
\[2sinx +1-2sinx+\sin^{2}x= 2-\cos^{2}x\]
Next you want to remove the terms that cancel out.
\[1+\sin^{2}x=2-\cos^{2}x\]
Change the sine term on the left side to a cosine term.
\[1+(1-\cos^{2}x)=2-\cos^{2}x\]
Distribute and add.
\[2-\cos^{2}x=2-\cos^{2}x\]

Answer 2

This is so helpful! Thank you! Can you take a look at one more?

Answer 3

@awesomelady2

Answer 4

\( cos\ x~(cos\ x-sec~x)= cos^2x-1=-(1-cos^2x)=-sin^2x\)

So yes. It is an identity