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Maths-

General

Easy

Question

The number of solution of $sin to the power of 4 end exponent invisible function application x minus cos to the power of 2 end exponent invisible function application x sin invisible function application x plus 2 sin to the power of 2 end exponent invisible function application x plus sin invisible function application x equals 0$ in $0 less or equal than x less or equal than 3 pi$ is

3
4
5
6

The correct answer is: 4

$sin to the power of 4 end exponent invisible function application x minus cos to the power of 2 end exponent invisible function application x sin invisible function application x plus 2 sin to the power of 2 end exponent invisible function application x plus sin invisible function application x equals 0$
$rightwards double arrow sin invisible function application x open square brackets sin to the power of 3 end exponent invisible function application x minus cos to the power of 2 end exponent invisible function application x plus 2 sin invisible function application x plus 1 close square brackets equals 0$
$rightwards double arrow sin invisible function application x open square brackets sin to the power of 3 end exponent invisible function application x minus 1 plus sin to the power of 2 end exponent invisible function application x plus 2 sin invisible function application x plus 1 close square brackets equals 0$
$rightwards double arrow sin invisible function application x open square brackets sin to the power of 3 end exponent invisible function application x plus sin to the power of 2 end exponent invisible function application x plus 2 sin invisible function application x close square brackets equals 0$
$rightwards double arrow sin to the power of 2 end exponent invisible function application x equals 0$ or $sin to the power of 2 end exponent invisible function application x plus sin invisible function application x plus 2 equals 0 blank$ (not possible for real $x$ )
$rightwards double arrow sin invisible function application x equals 0$
Hence, the solutions are $x equals 0 comma blank pi comma blank 2 pi comma 3 pi$

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