JEE Advanced 2015 · Paper 1 · Mathematics Q41

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MathematicsInteger+4Question 41 of 60

The number of distinct solutions of the equation
$\frac54\cos^22x+\cos^4x+\sin^4x+\cos^6x+\sin^6x=2$
in the interval $[0,2\pi]$ is

Your answer

Answer and worked solution

Official answer: 8

Simplify. $\sin^4x+\cos^4x=1-\frac12\sin^22x$ and $\sin^6x+\cos^6x=1-\frac34\sin^22x$ . The equation becomes
$\frac54\cos^22x+2-\frac54\sin^22x=2\implies\cos4x=0.$

Solutions. $x=\dfrac\pi8+\dfrac{k\pi}4$ . In $[0,2\pi]$ , $k=0,1,\dots,7$ gives 8 solutions.

Answer: 8

Topics:Trigonometric equations Trigonometric ratios and identities

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JEE Advanced 2015 · Paper 1, Mathematics question 41