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Maths-

General

Easy

Question

The number of values of $theta$ which satisfy the equation $sin invisible function application 3 theta minus sin invisible function application theta equals 4 cos to the power of 2 end exponent invisible function application theta minus 2 comma blank for all blank theta element of open square brackets 0 comma blank 2 pi close square brackets comma$ is

4
5
7
0

The correct answer is: 5

$3 sin invisible function application theta minus 4 sin to the power of 3 end exponent invisible function application theta minus sin invisible function application theta equals 2 open parentheses 2 cos to the power of 2 end exponent invisible function application theta minus 1 close parentheses$
$rightwards double arrow 2 sin invisible function application theta open parentheses 1 minus 2 sin to the power of 2 end exponent invisible function application theta close parentheses equals 2 cos to the power of 2 end exponent invisible function application 2 theta$
$rightwards double arrow 2 cos invisible function application 2 theta open parentheses sin invisible function application theta minus 1 close parentheses equals 0$
$rightwards double arrow cos invisible function application 2 theta equals 0$ or $sin invisible function application theta equals 1$
$rightwards double arrow 2 theta equals open parentheses 2 n plus 1 close parentheses pi divided by 2$ or $blank theta equals 2 n pi plus pi divided by 2 comma blank for all blank n blank element of Z$
$rightwards double arrow theta equals open parentheses 2 n plus 1 close parentheses pi divided by 4 comma$ or $theta equals open parentheses 4 n plus 1 close parentheses pi divided by 2 comma blank for all blank n blank element of Z$
Hence, $theta equals pi divided by 4 comma blank 3 pi divided by 4 comma blank 5 pi divided by 4 comma blank 7 pi divided by 4 comma blank pi divided by 2. blank open parentheses because theta element of open square brackets 0 comma blank 2 pi close square brackets close parentheses$

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