If the equation sin^4 x + cos^4 x = a has rea | vedclass

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

Question

(B) Given the equation $\sin^4 x + \cos^4 x = a$. We can rewrite the expression as: $\sin^4 x + \cos^4 x = (\sin^2 x + \cos^2 x)^2 - 2 \sin^2 x \cos^2

Vedclass · Accepted Answer

$\frac{1}{2} \leq a \leq 1$

Vedclass · Answer

(B) Given the equation $\sin^4 x + \cos^4 x = a$. We can rewrite the expression as: $\sin^4 x + \cos^4 x = (\sin^2 x + \cos^2 x)^2 - 2 \sin^2 x \cos^2 x$ $= 1^2 - \frac{1}{2} (2 \sin x \cos x)^2$ $= 1 - \frac{1}{2} \sin^2(2x)$. Since $0 \leq \sin^2(2x) \leq 1$,we multiply by $-\frac{1}{2}$: $-\frac{1}{2} \leq -\frac{1}{2} \sin^2(2x) \leq 0$. Adding $1$ to all parts: $1 - \frac{1}{2} \leq 1 - \frac{1}{2} \sin^2(2x) \leq 1 + 0$ $\frac{1}{2} \leq a \leq 1$. Thus,the equation has real solutions when $\frac{1}{2} \leq a \leq 1$.

If the equation $\sin^4 x + \cos^4 x = a$ has real solutions,then:

Similar Questions

If $0 < \theta < \pi$,then the minimum value of $3 \sin \theta + \text{cosec}^3 \theta$ is

If $x + y + z = 180^\circ$,then $\cos 2x + \cos 2y - \cos 2z$ is equal to

If $\sin \theta = \frac{1}{2} \left( \sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} \right)$,where $x, y \in \mathbb{R} - \{0\}$. Then:

If $A+B+C=\frac{\pi}{4}$,then $4 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}-\cos \frac{\pi}{8}=$

If $f(x) = a \cos(bx + c) + d$,then the range of $f(x)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module