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

option D is correct.

Explanation:

we are given the function
`\sqrt{((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{((1-\cos \theta )(1+\cos \theta ))/(\cos ^2\theta )}=\sqrt{(\sin ^2\theta )/(\cos ^2\theta )}=√(\tan ^2\theta )=|\tan \theta |`

Hence, option D is correct.