The principal solution of of (5+3 θ)(2 θ+1)=0 are

Correct Answer is : 2π3,4π32 π/3, 4 π/332π,34π

Correct Answer is : 2π3,4π32 π/3, 4 π/332π,34π

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MHTCET 25 Apr 2025 Shift 1 Paper

Question : 115 of 150

Marks: +1, -0

(5+3 \sin \theta)(2 \cos \theta+1)=0

are

Solution:

Concept:

For a product to be zero, at least one factor must be zero. The principal solutions are the values of

\theta

[0, 2\pi)

satisfying the equation.

Explanation:

Given:

(5+3\sin\theta)(2\cos\theta+1)=0

So, either

5+3\sin\theta=0

2\cos\theta+1=0

First:

5+3\sin\theta=0 \Rightarrow \sin\theta=-\frac{5}{3}

This is not possible because

\sin\theta

always lies between

-1

and

1

Second:

2\cos\theta+1=0 \Rightarrow \cos\theta=-\frac{1}{2}

[0, 2\pi)

\cos\theta=-\frac{1}{2}

\theta=\frac{2\pi}{3}

and

\theta=\frac{4\pi}{3}

Therefore, the principal solutions are

\frac{2\pi}{3}

and

\frac{4\pi}{3}

Answer:

\frac{2\pi}{3}, \frac{4\pi}{3}

Hence, the correct option is C.

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