JEE MATHEMATICS MCQ: COMPOUND ANGLES

1 Easy

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Application +4 | -1

\mathrm{\;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 + {\left( {p - r} \right)^2}

Option B is correct because it represents the simplified expression after applying Vieta's formulas and trigonometric identities to the given equation.

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

and

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

, then the value of

\tan \,\,2A

is The value of

\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)

, is
The sides of a triangle are

\sin \alpha, \cos \alpha

and

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

for some

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

. Then, the greatest angle of the triangle is If

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

is equal to

If

A,B,C

are angles of a triangle, then the minimum value of

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

, is If

A > 0,\,\;B > 0

and

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

, then the maximum value of

\tan A\,\,\tan B

, is