Q53 / 90 · KVPY 2010 (SB/SX) · Mathematics

The number of roots of the equation $\cos ^{7} \theta-\sin ^{4} \theta=1$ that lie in the interval $[0,2 \pi]$ is-

Correct answer
A
2
B
3
C
4
D
8

Solution

$\quad \cos ^{7} \theta=1+\sin ^{4} \theta \geq 1$ but $\cos ^{7} \theta \leq 1$, so $\cos \theta=1 ; \sin \theta=0$ $$ =0,2 \pi $$

Hence, the correct answer is option: 'A'.

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