How do you verify $sintheta+costheta=(2sin^2theta-1)/(sintheta-costheta)$ ?

Question

3469 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-12T09:35:14

see below

$sin theta +cos theta=(2sin^2theta-1)/(sin theta-costheta)$

Left Side: $=sin theta +cos theta$

$=(sin theta +cos theta)/1*(sintheta-costheta)/(sintheta-costheta)$

$=(sin^2theta-cos^2theta)/(sin theta -cos theta)$

$=(sin^2theta-(1-sin^2theta))/(sin theta -cos theta)$

$=(sin^2theta-1+sin^2theta)/(sin theta -cos theta)$

$=(sin^2theta+sin^2theta-1)/(sin theta -cos theta)$

$=(2sin^2theta-1)/(sin theta -cos theta)$

$:.=$ Right Side

How do you verify sintheta+costheta=(2sin^2theta-1)/(sintheta-costheta)sintheta+costheta=(2sin^2theta-1)/(sintheta-costheta)?