JEE MATHEMATICS MCQ: COMPOUND ANGLES

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Application +4 | -1

\tan \alpha, \tan \beta, \tan \gamma

are the roots of the equation

x^3-p x^2-r=0

, then the value of

\left(1+\tan ^2 \alpha\right)\left(1+\tan ^2 \beta\right)\left(1+\tan ^2 \gamma\right)

is equal to

View answer and explanation

Correct option: B

1+(p-r)^2

Option B (

1+(p-r)^2

) is correct because it is the result of expanding and simplifying the expression

(1+\tan ^2 \alpha)(1+\tan ^2 \beta)(1+\tan ^2 \gamma)

using Vieta's formulas.

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