JEE MATHEMATICS MCQ: COMPOUND ANGLES

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Application +4 | -1

Let

A,\;B

and

C

are the angles of a teiangle and

\tan \left( {\frac{A}{2}} \right) = \frac{1}{3},\tan \left( {\frac{B}{2}} \right) = \frac{2}{3}

. Then,

\tan \left( {\frac{C}{2}} \right)

is equal to

View answer and explanation

Correct option: D

\mathrm{1}\,\mathrm{/}\,\mathrm{3}

Option A (

\mathrm{1}\,\mathrm{/}\,\mathrm{3}

) is incorrect. The correct answer is 7/9. The value of

\tan \left( {\frac{C}{2}} \right)

is found using the identity

\tan \frac{A}{2} \tan \frac{B}{2} + \tan \frac{B}{2} \tan \frac{C}{2} + \tan \frac{C}{2} \tan \frac{A}{2} = 1

in a triangle.

More Questions from COMPOUND ANGLES

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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