If $\;\;\frac{\pi }{2} < \alpha < \pi ,\,\,\pi < \beta < \,\,\frac{{3\pi }}{2};\,\,\sin \,\,\alpha = \frac{{15}}{{17}}\,\,\;{\rm{and}}\,\,\tan \,\,\beta = \frac{{12}}{5}$ then the value of $\sin \,\left( {\beta - \alpha } \right)$ is

JEE MATHEMATICS MCQ: COMPOUND ANGLES

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Application +4 | -1

\;\;\frac{\pi }{2} < \alpha < \pi ,\,\,\pi < \beta < \,\,\frac{{3\pi }}{2};\,\,\sin \,\,\alpha = \frac{{15}}{{17}}\,\,\;\mathrm{and}\,\,\tan \,\,\beta = \frac{{12}}{5}

then the value of

\sin \,\left( {\beta - \alpha } \right)

View answer and explanation

Correct option: D

\frac{{171}}{{221}}

Option D (

\frac{{171}}{{221}}

) is correct because, by using the given trigonometric values and the angle subtraction formula, we can calculate the value of

\sin(\beta - \alpha)

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\tan \left( {A + B} \right) = p

\tan \left( {A - B} \right) = q

\tan \,\,2A

\cos \,\,x\,\,\cos \,\,y\,\,\sin \,\,\left( {x - y} \right) + \cos \,\,y\,\,\cos \,\,z\,\,\sin \,\,\left( {y - z} \right)

+ \cos \,\,z\,\,\cos \,\,x\,\,\sin \,\,\left( {z - x} \right) + \sin \,\,\left( {x - y} \right)\sin \,\,\left( {y - z} \right)\,\,\sin \,\,\left( {z - x} \right)

\sin \alpha, \cos \alpha

\sqrt{1+\sin \alpha \cos \alpha}

0<\alpha<\frac{\pi}{2}

\tan \,\,A = 2\,\,\tan \,\,B + \cot \,\,B,\;\;\mathrm{then}\;\,2\,\,\tan \left( {A - B} \right)\mathrm{\;}

A,B,C

{\tan ^2}\,\,\frac{A}{2} + {\tan ^2}\,\,\frac{B}{2} + {\tan ^2}\,\,\frac{C}{2}

A > 0,\,\;B > 0

A + B = \frac{\pi }{3}

\tan A\,\,\tan B