JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Hard

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Analyzing +4 | -1

If the expression

\frac{{\sin \,\,\frac{x}{2}\,\, + \,\,\cos \,\,\frac{x}{2} - \,\,i\,\,\tan \,\,x}}{{1 + 2\,i\,\,\sin \,\,\frac{x}{2}}}

is real, then x is equal to

View answer and explanation

Correct option: C

2n\;\pi + 2{\tan ^{ - 1}}k

, where

k \in \left( {1,2} \right),\,\,n \in Z

Option C (

2n\\;\pi + 2{\tan ^{ - 1}}k

, where

k \in \left( {1,2} \right),\\,n \in Z

) is correct because it represents the solution for x when the given expression is real, derived by setting the imaginary part to zero.

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