Question

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Answer 1

`\large\boxed{\tan x(\cot x-\cos x)=1-\sin x}`

Explanation:

`Use\\\\(\tan x)(\cot x)=1\\\\\tan x=(\sin x)/(\cos x)\\\\\text{distributive property:}\ a(b-c)=ab-ac\\======================\\\\\tan x(\cot x-\cos x)=(\tan x)(\cot x)-(\tan x)(\cos x)\\\\=1-\left((\sin x)/(\cos x)\right)(\cos x)=1-\sin x`