Get the solution to "Verify the identity. cot2θ−cos2θ=cot2θcosθ"

Yasmin

Answered question

2021-09-07

Verify the identity.

\cot^{2} θ - \cos^{2} θ = \cot^{2} θ \cos^{θ}

Szeteib

Skilled2021-09-08Added 102 answers

Given:

\cot^{2} θ - \cos^{2} θ = \cot^{2} θ \cos^{θ}

Manipulating right side

\cot^{2} θ \cos^{2} θ

Rewrite using trigonometry identities:

\cos^{2} θ = 1 - \sin^{2} θ

= (1 - \sin^{2} θ) \cot^{2} θ

Expand

(1 - \sin^{2} θ) \cot^{2} θ : \cot^{2} θ - \cot^{2} θ \sin^{2} θ

= \cot^{2} θ - \cot^{2} θ \sin^{2} θ

Simplify using:

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

= \cot^{2} θ - \frac{\cos^{2} θ}{\sin^{θ}} \times \sin^{2} θ

= \cot^{2} θ - \cos^{θ}

We showed that the two sides could take the same form.
Hence proved

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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