If sin x-cos x-2- then sin nx-cos nx is equal to

The correct option is A 2 sin x + cosec x = 2 sin x + 1/sin x = 2 sin^2 x + nbsp;1 = 2sin x (sin x 1)^2 = 0 sin x = 1 Thus, c ...

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Standard XII

Mathematics

Range of Trigonometric Expressions

If sin x+co...

Question

If $sin x + cos sec x = 2,$ then ${sin}^{n} x + cos {sec}^{n} x$ is equal to

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2^{n}

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2^{n - 1}

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2^{n - 2}

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Solution

The correct option is A 2
$sin x + c o s e c x = 2$
$sin x + \frac{1}{sin x} = 2$
${sin}^{2} x + 1 = 2 sin x$
$(sin x - 1)^{2} = 0$
$sin x = 1$
Thus, $c o s e c x = 1$
Now, ${sin}^{n} x + c o s e c^{n} x = 1^{n} + 1^{n} = 2$

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If sinx+cossecx=2, then sinnx+cossecnx is equal to

The correct option is A 2sinx+cosecx=2sinx+1sinx=2sin2x+1=2sinx(sinx−1)2=0sinx=1Thus, cosecx=1Now, sinnx+cosecnx=1n+1n=2

If $sin x + cos sec x = 2,$ then ${sin}^{n} x + cos {sec}^{n} x$ is equal to

The correct option is A 2
$sin x + c o s e c x = 2$
$sin x + \frac{1}{sin x} = 2$
${sin}^{2} x + 1 = 2 sin x$
$(sin x - 1)^{2} = 0$
$sin x = 1$
Thus, $c o s e c x = 1$
Now, ${sin}^{n} x + c o s e c^{n} x = 1^{n} + 1^{n} = 2$