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3.Trigonometrical Ratios, Functions and Identities
easy
$\frac{{2\sin \theta \,\tan \theta (1 - \tan \theta ) + 2\sin \theta {{\sec }^2}\theta }}{{{{(1 + \tan \theta )}^2}}} = $
A
$\frac{{\sin \,\theta }}{{1 + \tan \theta }}$
B
$\frac{{2\,\sin \theta }}{{1 + \tan \theta }}$
C
$\frac{{2\sin \theta }}{{{{(1 + \tan \theta )}^2}}}$
D
इनमें से कोई नहीं
Solution
दिया गया व्यंजक
$ = \frac{{2\,\sin \theta }}{{{{(1 + \tan \,\theta )}^2}}}\,\{ \tan \,\theta \,(1 – \tan \,\theta ) + {\sec ^2}\theta \} $
$ = \frac{{2\,\sin \theta }}{{{{(1 + \tan \,\theta )}^2}}}\,\{ \tan \,\theta \, – {\tan ^2}\,\theta + 1 + {\tan ^2}\theta \} $
$ = \frac{{2\,\sin \theta }}{{1 + \tan \theta }}$.
Standard 11
Mathematics
