Question

Is the answer to tan^2x (cos^2x+1)+cos^2x=sec^2 just the left side equaling tan^2x+1? HELP PLEASE

Answer 1

Yes, it is as `tan^2x+1=sec^2x`

Explanation:

`tan^2x(cos^2x+1)+cos^2x`

= `tan^2xcos^2x+tan^2x+cos^2x`

= `tan^2xcos^2x+cos^2x+tan^2x`

= `(tan^2x+1)cos^2x+tan^2x`

= `sec^2xcos^2x+tan^2x`

And as `sec^2x=1/cos^2x`, we can write it as

`1/cos^2x xxcos^2x+tan^2x`

= `1+tan^2x`

= `sec^2x`