sin^ 2n x + cos^ 2n x lies between - Vidyadip

MCQ

$sin^{2n}x + cos^{2n}x$ lies between

A
$-1$ and $1$
✓
$0$ and $1$
C
$1$ and $2$
D
None of these

✓

Answer

Correct option: B.

$0$ and $1$

b
Since $0 \leq \sin ^{2 \pi} x \leq \sin ^{2} x$

$0 \leq \cos ^{2 \pi} x \leq \cos ^{2} x$

$\left[\because \sin ^{4} x=\sin ^{2} x, \sin ^{2} x \leq \sin ^{2} x \cdot 1\right.$

$\left.\therefore \sin ^{4} x \leq \sin ^{2} x \text { etc. }\right]$

$\Rightarrow \quad 0<\sin ^{2 \pi} x+\cos ^{2 n} x \leq \sin ^{2} x+\cos ^{2} x=1$

$\Rightarrow \quad 0<\sin ^{2 n} x+\cos ^{2 n} x \leq 1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the sum of the roots of the equation $a{x^2} + bx + c = 0$ be equal to the sum of the reciprocals of their squares, then $b{c^2},\;c{a^2},\;a{b^2}$ will be in

The length intercepted by the curve ${y^2} = 4x$ on the line satisfying $dy/dx = 1$ and passing through point $(0, 1)$ is given by

$\int_0^{\pi /2} {{{\sin }^4}x{{\cos }^6}x\,dx} $ equals

Let $S_{n}=1 \cdot(n-1)+2 \cdot(n-2)+3 \cdot(n-3)+\ldots+$ $(\mathrm{n}-1) \cdot 1, \mathrm{n} \geq 4$

The sum $\sum_{n=4}^{\infty}\left(\frac{2 S_{n}}{n !}-\frac{1}{(n-2) !}\right)$ is equal to :

Let the system of linear equations $x +2 y + z =2$, $\alpha x +3 y - z =\alpha,-\alpha x + y +2 z =-\alpha$ be inconsistent. Then $\alpha$ is equal to

The minimum value of ${\left( {{x_1} - {x_2}} \right)^2} + {\left( {\sqrt {2 - x_1^2} - \frac{9}{{{x_2}}}} \right)^2}$ where ${x_1} \in \left( {0,\sqrt 2 } \right)$ and ${x_2} \in {R^ + }$.

$\int_{}^{} {\frac{{dx}}{{{e^x} - 1}} = } $

Let a triangle $A B C$ be inscribed in the circle $x ^{2}-$ $\sqrt{2}(x+y)+y^{2}=0$ such that $\angle B A C=\frac{\pi}{2}$. If the length of side $A B$ is $\sqrt{2}$, then the area of the $\triangle ABC$ is equal to

$\int_{\,0}^{\,1000} {{e^{x - [x]}}dx} $ is

Let $A=\left\{\theta \in R:\left(\frac{1}{3} \sin \theta+\frac{2}{3} \cos \theta\right)^2=\frac{1}{3} \sin ^2 \theta+\frac{2}{3} \cos ^2 \theta\right\}$.Then