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

If cos $\frac{x}{2}$ , cos $\frac{x}{2^{2}}$ , cos $\frac{x}{2^{3}}$ .............cos $\frac{x}{2^{n}}$ = $\frac{s i n x}{2^{n} s i n \frac{x}{2^{n}}}$ Then

$\frac{1}{2}$ tan $\frac{x}{2}$ + $\frac{1}{2^{2}}$ tan $\frac{x}{2^{2}}$ + ............. $\frac{1}{2^{n}}$ tan $\frac{x}{2^{n}}$ is

Q. If

(1 + x)^{2 n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{2 n} x^{2 n}

then

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If sinx+cscx=2, then sinnx+cscnx is equal to ?

The correct option is B 2sinx+(1sinx)=2usingAM≥GMitispossibleonlywhensinx=1/sinx∴sinx=1∴sinna+cosnx=1+1=2

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

The correct option is B $2$
$s i n x + (\frac{1}{s i n x}) = 2 u s i n g A M \geq G M i t i s p o s s i b l e o n l y w h e n s i n x = 1 / s i n x ∴ s i n x = 1 ∴ s i n^{n} a + c o s^{n} x = 1 + 1 = 2$