## Trending News

Promoted

# sinxsecx=tanx????? cos^2(2x)-sin^2(2x)=cos(4x)???? please help with these two problems?

### 1 Answer

Relevance

- Seamus OLv 71 decade agoFavorite Answer
LHS = sinx secx

= sinx (1/cosx)

= sinx / cosx

= tanx

= RHS

so sinx secx = tanx

cos^2 (2x) - sin^2 (2x) = cos(4x)

For this one I'm going to use the trig identities:

cos(2x) = 2cos^2 x - 1 which can be rewritten cos^2 x = (1/2)[cos(2x) + 1]

and cos(2x) = 1 - 2sin^2 x which can be rewritten sin^2 x = (1/2)[1 - cos(2x)]

and substituting 2x for x in the identities like this:

LHS = cos^2(2x) - sin^2(2x)

= (1/2) [cos(4x) + 1] - (1/2)[1 - cos(4x)]

= (1/2)cos(4x) + 1/2 - 1/2 + (1/2)cos(4x)

= cos(4x)

= RHS

so cos^2 (2x) - sin^2 (2x) = cos(4x)

Still have questions? Get your answers by asking now.