JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q25

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MathematicsInteger+4 / -1Question 25 of 90

If the sum of solutions of the system of equations $2\sin^2\theta-\cos2\theta=0$ and $2\cos^2\theta+3\sin\theta=0$ in the interval $[0,2\pi]$ is $k\pi$ , then $k$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 3

First equation. $2\sin^2\theta-(1-2\sin^2\theta)=0$ : $\sin^2\theta=\frac14$ .

Second. $2-2\sin^2\theta+3\sin\theta=0$ : $\sin\theta=-\frac12$ (2 is impossible).

Common solutions $\frac{7\pi}6,\frac{11\pi}6$ , sum $3\pi$ .

Answer: 3

Topics:Trigonometric equations

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JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 25