Resolved: "Verify the identify. tan2θsec⁡θ+1=1−cos⁡xcos⁡x"

coexpennan

Answered question

2021-09-12

Verify the identify.

\frac{\tan^{2} θ}{\sec θ + 1} = \frac{1 - \cos x}{\cos x}

Laith Petty

Skilled2021-09-13Added 103 answers

Solution:

L H S = \frac{\tan^{2} θ}{\sec θ + 1}

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

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

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

= \frac{(1 - \cos^{2} θ)}{\cos θ (1 + \cos θ)}

= \frac{(1 - \cos θ) (1 + \cos θ)}{\cos θ (1 + \cos θ)}

= \frac{1 - \cos θ}{\cos θ}

= R H S

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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