If ${\rm{If}}\,\,\tan \,\,\alpha = {\left( {1 + {2^{ - x}}} \right)^{ - 1}},\,\,\tan \,\,\beta = {\left( {1 + {2^{x + 1}}} \right)^{ - 1}},\;\,{\rm{then}}\;\,\,\alpha + \beta \;$ equals

JEE MATHEMATICS MCQ: COMPOUND ANGLES

1 Easy

1 of 1

Application +4 | -1

\mathrm{If}\,\,\tan \,\,\alpha = {\left( {1 + {2^{ - x}}} \right)^{ - 1}},\,\,\tan \,\,\beta = {\left( {1 + {2^{x + 1}}} \right)^{ - 1}},\;\,\mathrm{then}\;\,\,\alpha + \beta \;

equals

View answer and explanation

Correct option: B

\frac{\pi }{4}

Option B (

\frac{\pi }{4}

) is correct because by using the tangent addition formula,

\tan(\alpha + \beta)

simplifies to 1, hence

\alpha + \beta = \frac{\pi}{4}

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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