In a $Δ A B C . A > B$ and $A, B$ satisfy the equation $3 sin x - 4 {sin}^{3} x = K$ and $0 < K < 1$ then angle $C$ is equal to

\frac{- π}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- π}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 π}{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{4 π}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{2 π}{3}$
We have,

$3 sin x - 4 {sin}^{3} x = k$

$sin 3 x = k$

$Now,We know that$

$∴ sin 3 A = s i n 3 B$

$sin 3 A = sin (180^{o} - 3 B)$

$Now,$

$3 A = 180^{o} - 3 B$

$A = 60^{o} - B$

$∴ A + B = 60^{o}$

Then,

$A + B + C = 180^{o}$

$C = 180^{o} - (A + B)$

$C = 180^{o} - 60^{o}$

$C = 120^{o}$

$C = \frac{2 π}{3}$

Hence, this is the answer.

Suggest Corrections

Similar questions

In a triangle ABC, angle A is greater than B. If the measures of angles A and B satisfy the equation $3 s i n x - 4 s i n^{3} x = k, 0 < k < 1$ , then the value of angle C is

Q. In a

Δ A B C, ∠ A < ∠ B

. If

sin A

and

sin B

satisfy the equation

3 sin x - 4 {sin}^{3} x - k = 0

, where

0 < K < 1

, then find measure of

∠ C

Q. In a

Δ A B C, ∠ A > ∠ B .

sin A

and

sin B

satisfy the equation

3 sin x - 4 {sin}^{3} x - k = 0, 0 < k < 1,

then

∠ C

Q. In a triangle ABC angle A is greater than angle B . if the measure of angle A and B satisfy the equation

3 sin x - 4 {sin}^{3} x - k = 0, 0 < k < 1

, then the measure of angle C is

Q. In a triangle ABC , the angle B is greater than angle A, if the values of the angle A and B satisfy the equation 3sinx 4

s i n^{3}

x k = 0 , 0 < k < 1 , then value of C is

Join BYJU'S Learning Program

In a ΔABC.A>B and A,B satisfy the equation 3sinx−4sin3x=K and 0<K<1 then angle C is equal to

The correct option is C 2π3We have, 3sinx−4sin3x=k sin3x=k Now,Weknowthat ∴sin3A=sin3B sin3A=sin(180o−3B) Now, 3A=180o−3B A=60o−B ∴A+B=60o Then, A+B+C=180o C=180o−(A+B) C=180o−60o C=120o C=2π3 Hence, this is the answer.

In a $Δ A B C . A > B$ and $A, B$ satisfy the equation $3 sin x - 4 {sin}^{3} x = K$ and $0 < K < 1$ then angle $C$ is equal to