If sin x + csc x = 2,then sin^n x + csc^n x i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the equation: $\sin x + \csc x = 2$.Since $\csc x = \frac{1}{\sin x}$,we can write the equation as $\sin x + \frac{1}{\sin x} = 2$.Multiplyi

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Given the equation: $\sin x + \csc x = 2$.Since $\csc x = \frac{1}{\sin x}$,we can write the equation as $\sin x + \frac{1}{\sin x} = 2$.Multiplying by $\sin x$,we get $\sin^2 x + 1 = 2 \sin x$,which simplifies to $\sin^2 x - 2 \sin x + 1 = 0$.This is a perfect square: $(\sin x - 1)^2 = 0$.Therefore,$\sin x = 1$.Since $\sin x = 1$,then $\csc x = \frac{1}{1} = 1$.Substituting these values into the expression $\sin^n x + \csc^n x$,we get $1^n + 1^n = 1 + 1 = 2$.

If $\sin x + \csc x = 2$,then $\sin^n x + \csc^n x$ is equal to

Similar Questions

Given that $\cos \left( \frac{\alpha - \beta}{2} \right) = 2\cos \left( \frac{\alpha + \beta}{2} \right)$,then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2}$ is equal to

Evaluate: $\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$

Let $f(x) = \max (\sin x, \cos x)$ and $g(x) = \min (\cos x, \sin x)$. If the equation $f(x)y^2 + ay + g(x) = 0$ has real roots for all $x \in R$,then the complete set of values of $a$ is:

If $\sin \theta = \frac{3}{5},$ then the value of $\frac{\tan \theta + \cos \theta}{\cot \theta + \operatorname{cosec} \theta}$ is equal to

If $\tan \theta - \cot \theta = 0$ and $\theta$ is a positive acute angle,then the value of $\frac{\tan (\theta + 15^{\circ})}{\tan (\theta - 15^{\circ})}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module