JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q30

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MathematicsInteger+4 / -1Question 30 of 90

Let $S_1=\left\{x\in[0,12\pi]:\sin^5x+\cos^5x=1\right\}$ and $S_2=\left\{x\in[0,8\pi]:\sin^7x+\cos^7x=1\right\}$ . Then $n(S_1)-n(S_2)$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 4

Equality $\sin^nx+\cos^nx=1$ ( $n=5,7$ ) only when one of them is 1 and the other 0: $x=2k\pi$ or $\frac\pi2+2k\pi$ .

Counts. $[0,12\pi]$ : $7+6=13$ . $[0,8\pi]$ : $5+4=9$ . Difference 4.

Answer: 4

Topics:Trigonometric equations

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 30