(B) Since $A, B, C$ are in $A.P.$,we have $A + C = 2B$. Given $A + B + C = 180^o$,substituting $A + C = 2B$ gives $3B = 180^o$,so $B = 60^o$. Given $\

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(B) Since $A, B, C$ are in $A.P.$,we have $A + C = 2B$. Given $A + B + C = 180^o$,substituting $A + C = 2B$ gives $3B = 180^o$,so $B = 60^o$. Given $\sin(2A + B) = \frac{1}{2}$,we have $2A + 60^o = 30^o$ or $150^o$. Since $A$ must be positive,$2A + 60^o = 150^o$ implies $2A = 90^o$,so $A = 45^o$. Using $A + C = 2B$,we get $45^o + C = 120^o$,which gives $C = 75^o$. Thus,the angles are $45^o, 60^o, 75^o$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

Easy

$ABC$ is a triangle such that $\sin(2A + B) = \sin(C - A) = -\sin(B + 2C) = \frac{1}{2}$. If $A, B,$ and $C$ are in $A.P.$,then $A, B,$ and $C$ are:

A
$30^o, 60^o, 90^o$
B
$45^o, 60^o, 75^o$
C
$45^o, 45^o, 90^o$
D
$60^o, 60^o, 60^o$

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Trigonometrical Ratios, Functions and Identities

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Mix Examples-Trigonometrical Ratios, Functions and Identities

If $\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin \alpha}{\cos x} - \frac{2}{1 + \cos x}$,then $\alpha = $

Easy

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If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

EasyTS EAMCET 2001

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If $\sin \alpha - \cos \alpha = m$ and $\sin 2 \alpha = n - m^2$,where $-\sqrt{2} \leq m \leq \sqrt{2}$,then $n$ is equal to

MediumAP EAMCET 2021

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If $\sin \theta + \cos \theta = 1$,then $\sin \theta \cos \theta = $

Easy

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The value of $\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}$ is :

DifficultTS EAMCET 2003

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$ABC$ is a triangle such that $\sin(2A + B) = \sin(C - A) = -\sin(B + 2C) = \frac{1}{2}$. If $A, B,$ and $C$ are in $A.P.$,then $A, B,$ and $C$ are:

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If $\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin \alpha}{\cos x} - \frac{2}{1 + \cos x}$,then $\alpha = $

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

If $\sin \alpha - \cos \alpha = m$ and $\sin 2 \alpha = n - m^2$,where $-\sqrt{2} \leq m \leq \sqrt{2}$,then $n$ is equal to

If $\sin \theta + \cos \theta = 1$,then $\sin \theta \cos \theta = $

The value of $\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}$ is :

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