- #1

ytx123

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## Homework Statement

(tanx - cosecx)

^{2}- (cotx - secx)

^{2}= 2(cosecx - secx)

## Homework Equations

tanx = sinx/cosx

cotx = 1/tanx = cosx/sinx

cosecx = 1/sinx

secx = 1/cosx

## The Attempt at a Solution

LHS = (tanx-cosecx)(tanx-cosecx) - (cotx-secx)(cotx-secx)

= tan

^{2}x - tanxcosecx - tanxcosecx + cosec

^{2}x - cot

^{2}x + cotxsecx + cotxsecx

= sin

^{2}x/cos

^{2}x - (sinx/cosx)(1/sinx) - (sinx/cosx)(1/sinx) + 1/sin

^{2}x - cos

^{2}x/sin

^{2}x + (cosx/sinx)(1/cosx) + (cosx/sinx)(1/cosx) - (1/cos

^{2}x)

= sin

^{2}x/cos

^{2}x - 2sinx/sinxcosx + 1/sin

^{2}x - cos

^{2}x/sin

^{2}x + 2cosx/sinxcosx - 1/cos

^{2}x

= sin

^{2}x-1 / cos

^{2}x + 1 - cos

^{2}x / sin

^{2}x - 2sinx+2cosx/sinxcosx

= -1 + 1 - 2sinx+2cosx / sinxcosx

= 2sinx + 2cosx / sinxcosx

and I'm stucked

help thanks in advance :)

ps. if i post in the wrong place I am sry cos I am new :/