JEE MATHEMATICS MCQ: COMPOUND ANGLES

1 Easy

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Analyzing +4 | -1

If angle

\theta

be divided into two parts such that the tangent of one part is

k

times the tangent of the other and

\phi

is their difference, then

\mathrm{sin \theta }

is equal to

View answer and explanation

Correct option: A

\frac{{k + 1}}{{k - 1}}\,\,\sin \,\,\phi

Option A (

\frac{{k + 1}}{{k - 1}}\,\sin \,\phi

) is correct because by using componendo and dividendo rule on the given condition and applying trigonometric identities, we can express

\sin \theta

in terms of

k

and

\sin \phi

More Questions from COMPOUND ANGLES

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

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\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