Question

a) Explain the method for proving sinxtanx+ sin x/ tan x =1/ cos x b) Prove the identity

Answer 1

Part a

Rewrite tan x in terms of sin x and cos x

Part b

`\sin x \tan x+(\sin x)/(\tan x)\\\\=\sin x \cdot (\sin x)/(\cos x)+(\sin x)/((\sin x)/(\cos x))\\\\=\sin x \cdot (\sin x)/(\cos x)+(1)/((1)/(cos x))\\\\=(\sin^2 x)/(\cos x)+\cos x\\\\=(\sin^2 x+\cos^2 x)/(\cos x)\\\\=(1)/(\cos x)`