Question

Prove the identity
(cosxcotx) ÷ (cosx + cotx) = secx - tanx
Answered by Damon
sin x / cos x = tan x
and cos x/ sin x = ctn x

so what on earth is this?

1 / (cosx / sinx)

Using the reciprocal identity, cosx/sinx is equal to secx:

1 / secx

Which is equal to secx.
Answered by Damon
prove:
(cosxcotx) ÷ (cosx + cotx) = secx - tanx
===========================================
( cos x cos x /sin x ) / (cos x + cos x /sin x) ?= ? 1/cos x - sin x/cos x
cos x cos x / (sin x cos x + cos x) ?=? (1-sin x)/ cos x
cos x / ( sin x + 1) ?=? (1-sin x)/cos x
cos^2 x ?=? (1 + sin x) (1- sin x)
cos^2 x ?=? 1 - sin^2 x
cos^2 x + sin^2 x = 1 SURE ENOUGH
Answered by Damon
Good grief bot !
Answered by Damon
ah bot, yes but check my way.
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