JEE MATHEMATICS MCQ: COMPOUND ANGLES

1 Easy

1 of 1

Application +4 | -1

\sin ^{2} 5^{0}+\sin ^{2} 10^{\circ}+\sin ^{2} 15^{\circ}+\ldots \ldots .+\sin ^{2} 90^{\circ}=

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Correct option: C

9 \frac{1}{2}

Option C (9 1/2) is correct because pairing terms using the identity sin²(x) + sin²(90-x) = 1 simplifies the sum, and accounting for the remaining terms leads to the correct result.

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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

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