Question

Simplify square root parenthesis 1 minus cosine theta parenthesis times parenthesis 1 plus cosine theta parenthesis divided by cosine squared theta A. square root sine theta B. ±sin Θ C. ±cos Θ D. |tan Θ|

Answer 1

The answer is D.  |tan Θ|

√[(1 − cos θ)(1+cos θ)] / cos^2 θ
√(1 - cos^2 θ) /  cos^2 θ
  |tan Θ|

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Answer 2

Answer:

option D is correct.

Step-by-step explanation:

we are given the function $\sqrt{\frac{(1-\cos \theta )(1+\cos \theta )}{\cos ^2\theta }}$

we know that the expansion is given by $(1-\cos \theta )(1+\cos \theta )=1-\cos ^2\theta =\sin ^2\theta$

so $\sqrt{\frac{(1-\cos \theta )(1+\cos \theta )}{\cos ^2\theta }}=\sqrt{\frac{\sin ^2\theta }{\cos ^2\theta }}=\sqrt{\tan ^2\theta }=|\tan \theta |$

Hence, option D is correct.