Question

PLEASE HELP ASAP

prove the identity:
sec x sin x
—————— =sin^2x
tan x+cot x
Options in pic

Answer 1

See below

Explanation:

`\displaystyle (\sec x\sin x)/(\tan x+\cot x)\\\\=((1)/(\cos x) \sin x)/((\sin x)/(\cos x) + (\cos x)/(\sin x))\\ \\=((\sin x)/(\cos x) )/((\sin x \sin x)/(\cos x \sin x) + (\cos x \cos x)/(\cos x \sin x))\\\\=((\sin x)/(\cos x) )/((\sin^2 x)/(\cos x \sin x) + (\cos^2 x)/(\cos x \sin x))\\\\=((\sin x)/(\cos x))/((\sin^2 x+\cos^2 x)/(\cos x \sin x) )\\ \\=((\sin x)/(\cos x) )/((1)/(\cos x \sin x) )`

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

Thus, the identity is proven. Match the options up accordingly to my step-by-step process.