The number of roots of the equation cos ^7 th | vedclass

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Question

(a)

We have, $\cos ^7 	heta-\sin ^4 	heta=1$

$\Rightarrow \quad \cos ^7 	heta=1+\sin ^4 	heta$

LHS $\cos ^7 	heta \in[-1,1]$

$RHS \ge

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(a)

We have, $\cos ^7 	heta-\sin ^4 	heta=1$

$\Rightarrow \quad \cos ^7 	heta=1+\sin ^4 	heta$

LHS $\cos ^7 	heta \in[-1,1]$

$RHS \geq 1$

Hence, $\cos ^7 	heta=1$ and $\sin ^4 	heta=0$ $	herefore 	heta=0,2 \pi$ in $[0,2 \pi]$

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

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