# Trig identity (sinx+cosx)^2tanx = tanx+2sin^2x [Solved!]

### My question

Show (sinx+cosx)^2tanx=tanx+2sin^2x

### Relevant page

1. Trigonometric Identities

### What I've done so far

RHS = tanx+2sin^2x

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

=tanx + 2 - 2cos^2 x

But I can't make it look like the LHS.

X

Show (sinx+cosx)^2tanx=tanx+2sin^2x
Relevant page

<a href="/analytic-trigonometry/1-trigonometric-identities.php">1. Trigonometric Identities</a>

What I've done so far

RHS = tanx+2sin^2x

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

=tanx + 2 - 2cos^2 x

But I can't make it look like the LHS.

## Re: Trig identity (sinx+cosx)^2tanx = tanx+2sin^2x

It's correct so far, but I don't think it helped.

Expand out the bracket on the LHS and see if you recognize anything.

X

It's correct so far, but I don't think it helped.

Expand out the bracket on the LHS and see if you recognize anything.

## Re: Trig identity (sinx+cosx)^2tanx = tanx+2sin^2x

OK.

 (sinx+cosx)^2tanx  = (sin^2x + 2sinx cosx + cos^2 x)tanx

=(1 + 2sinxcosx)tanx

Is that right? But what do I do now?

X

OK.

(sinx+cosx)^2tanx  = (sin^2x + 2sinx cosx + cos^2 x)tanx

=(1 + 2sinxcosx)tanx

Is that right? But what do I do now?

## Re: Trig identity (sinx+cosx)^2tanx = tanx+2sin^2x

Just remember tanx = (sinx)/(cosx)

X

Just remember tanx = (sinx)/(cosx)

## Re: Trig identity (sinx+cosx)^2tanx = tanx+2sin^2x

(1+2sinxcosx)tanx =(1+2sinxcosx)(sinx)/(cosx)

= (sinx)/(cosx) + 2sin^2x

=tanx + 2sin^2 x

=RHS

Thanks a lot.

X

(1+2sinxcosx)tanx =(1+2sinxcosx)(sinx)/(cosx)

= (sinx)/(cosx) + 2sin^2x

=tanx + 2sin^2 x

=RHS

Thanks a lot.

## Re: Trig identity (sinx+cosx)^2tanx = tanx+2sin^2x

You're welcome!

X

You're welcome!