(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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Class 11

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Trigonometrical Ratios, Functions and Identities

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Mix Examples-Trigonometrical Ratios, Functions and Identities

If $\sin (\alpha+\beta)=5 \sin (\alpha-\beta)$,then $\frac{\sin 2 \beta}{5-\cos 2 \beta}=$

MediumAP EAMCET 2023

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If a regular pentagon and a regular decagon have the same perimeter,then the ratio of their areas is

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If the sides of a right-angled triangle are ${\cos2\alpha + \cos2\beta + 2\cos(\alpha + \beta )}$ and ${\sin2\alpha + \sin2\beta + 2\sin(\alpha + \beta )}$,then the length of the hypotenuse is:

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The number of elements in the set $S = \{x \in R : 2 \cos \left(\frac{x^{2}+x}{6}\right) = 4^{x} + 4^{-x}\}$ is $.....$

MediumJEE MAIN 2022

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If $\cosh x = \operatorname{cosec} \theta$,then $\coth^2 \frac{x}{2} = $

DifficultAP EAMCET 2023

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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:

Similar Questions

If $\sin (\alpha+\beta)=5 \sin (\alpha-\beta)$,then $\frac{\sin 2 \beta}{5-\cos 2 \beta}=$

If a regular pentagon and a regular decagon have the same perimeter,then the ratio of their areas is

If the sides of a right-angled triangle are ${\cos2\alpha + \cos2\beta + 2\cos(\alpha + \beta )}$ and ${\sin2\alpha + \sin2\beta + 2\sin(\alpha + \beta )}$,then the length of the hypotenuse is:

The number of elements in the set $S = \{x \in R : 2 \cos \left(\frac{x^{2}+x}{6}\right) = 4^{x} + 4^{-x}\}$ is $.....$

If $\cosh x = \operatorname{cosec} \theta$,then $\coth^2 \frac{x}{2} = $

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