If in a ${\rm{\;in\;a\;}}\,\Delta {\rm{\;}}ABC,\,\;\angle C = 90^\circ $, then the maximum value of $\sin \,\,A\,\,\sin \,\,B\;\,{\rm{is}}$

${\rm{None\;}}\,\,{\rm{of}}\,\,{\rm{these}}$

JEE MATHEMATICS MCQ: COMPOUND ANGLES

1 Easy

1 of 1

Application +4 | -1

If in a

\mathrm{\;in\;a\;}\,\Delta \mathrm{\;}ABC,\,\;\angle C = 90^\circ

, then the maximum value of

\sin \,\,A\,\,\sin \,\,B\;\,\mathrm{is}

View answer and explanation

Correct option: A

\frac{1}{2}

Option A (

\frac{1}{2}

) is correct because the maximum value of

\sin A \sin B

is found using trigonometric identities and the fact that

A + B = 90^\circ

Practice All Chapter MCQs →

\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