Get the solution to "Verify the identify. csc2θ1+tan2θ=cot2θ"

Ernstfalld

Answered question

2021-09-01

Verify the identify.

\frac{\csc^{2} θ}{1 + \tan^{2} θ} = \cot^{2} θ

Mayme

Skilled2021-09-02Added 103 answers

We know that

\cot x = \frac{\cos x}{\sin x}

\tan x = \frac{\sin x}{\cos x}

\sin^{2} x + \cos^{2} x = 1

L H S = \frac{\csc^{2} θ}{1 + \tan^{2} θ}

= \frac{\frac{1}{\sin^{2} θ}}{1 + \frac{\sin^{2} θ}{\cos^{2} θ}}

= \frac{\frac{1}{\sin^{2} θ}}{\frac{\cos^{2} θ + \sin^{2} θ}{\cos^{2} θ}}

= \frac{\frac{1}{\sin^{2} θ}}{\frac{1}{\cos^{2} θ}}

= {(\frac{\cos θ}{\sin θ})}^{2}

= \cot^{2} θ

= R H S

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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