First slide

Trigonometric equations

Question

Number of solutions of ${(\cos x)}^{5} + {(\sin x)}^{3} = 1$ in $[0, 2 π]$

Easy

A

1
B

3
C

2
D

no solution

Solution

${(\cos x)}^{5} + {(\sin x)}^{3} = 1$ exists only for $x = 0, \frac{π}{2}, 2 π$
$∴$ Number of solutions =3

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