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Trigonometric Functions and Equations question

2017 · Shift 2 · Q29

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JEE Advanced
Mathematics
Trigonometric Functions and Equations
2017 · Shift 2 · Q29

Trigonometric Functions and Equations question

2017 · Shift 2 · Q29

JEE AdvancedMathematicsTrigonometric Functions and EquationsMultiple correct+4 / −2

Let

\alpha

and

\beta

be non zero real numbers such that

2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \beta = 1

. Then which of the following is/are true?

A
$\sqrt 3 \tan \left( {{\alpha \over 2}} \right) - \tan \left( {{\beta \over 2}} \right) = 2$
B
$\tan \left( {{\alpha \over 2}} \right) - \sqrt 3 \tan \left( {{\beta \over 2}} \right) = 0$
C
$\tan \left( {{\alpha \over 2}} \right) + \sqrt 3 \tan \left( {{\beta \over 2}} \right) = 0$
D
$\sqrt 3 \tan \left( {{\alpha \over 2}} \right) + \tan \left( {{\beta \over 2}} \right) = 2$

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