If cos left( {α + β } right) = frac{4}{5} and sin left( {α

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3.Trigonometrical Ratios, Functions and Identities

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If $\cos \left( {\alpha + \beta } \right) = \frac{4}{5}$ and $\sin \left( {\alpha - \beta } \right) = \frac{5}{{13}}$,where $0 \le \alpha ,\beta \le \frac{\pi }{4}$ . Then $\tan 2\alpha =$

$\frac{{16}}{{63}}$

$\frac{{56}}{{33}}$

$\frac{{28}}{{33}}$

None of these

(AIEEE-2010) (IIT-1979)

Solution

$\cos \,(\alpha \, + \beta ) = \frac{4}{5} \Rightarrow \tan (\alpha \, + \beta ) = \frac{3}{4}$

$\sin \,(\alpha \, – \beta )\, = \frac{5}{{13}} \Rightarrow \tan \,(\alpha \, – \beta ) = \frac{5}{{12}}$

$\tan 2\alpha \, = \tan [(\alpha \, + \beta ) + (\alpha \, – \beta )]$ $\, = \,\frac{{\frac{3}{4} + \frac{5}{{12}}}}{{1 – \frac{3}{4}.\frac{5}{{12}}}} = \frac{{56}}{{33}}$

Standard 11

Mathematics

In triangle $ABC$, the value of $\sin 2A + \sin 2B + \sin 2C$ is equal to

easy

${(\cos \alpha + \cos \beta )^2} + {(\sin \alpha + \sin \beta )^2} = $

easy

If $\tan A = \frac{1}{2},\tan B = \frac{1}{3},$ then $\cos 2A = $

easy

The expression $[1 – sin (3\pi – \alpha ) + cos (3\pi + \alpha )]$ $\left[ {1\,\, – \,\,\sin \,\left( {\frac{{3\,\pi }}{2}\,\, – \,\,\alpha } \right)\,\, + \,\,\cos \,\left( {\frac{{5\,\pi }}{2}\,\, – \,\,\alpha } \right)} \right]$ when simplified reduces to :

normal

$\tan \frac{A}{2}$ is equal to

easy

If $\cos \left( {\alpha + \beta } \right) = \frac{4}{5}$ and $\sin \left( {\alpha - \beta } \right) = \frac{5}{{13}}$,where $0 \le \alpha ,\beta \le \frac{\pi }{4}$ . Then $\tan 2\alpha =$

Solution

Similar Questions

In triangle $ABC$, the value of $\sin 2A + \sin 2B + \sin 2C$ is equal to

${(\cos \alpha + \cos \beta )^2} + {(\sin \alpha + \sin \beta )^2} = $

If $\tan A = \frac{1}{2},\tan B = \frac{1}{3},$ then $\cos 2A = $

The expression $[1 – sin (3\pi – \alpha ) + cos (3\pi + \alpha )]$ $\left[ {1\,\, – \,\,\sin \,\left( {\frac{{3\,\pi }}{2}\,\, – \,\,\alpha } \right)\,\, + \,\,\cos \,\left( {\frac{{5\,\pi }}{2}\,\, – \,\,\alpha } \right)} \right]$ when simplified reduces to :

$\tan \frac{A}{2}$ is equal to

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