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 $A+B+C=\frac{\pi}{3}$,then $\sin \left(\frac{\pi-6A}{6}\right)+\sin \left(\frac{\pi-6B}{6}\right)+\sin C=$

The minimum value of $27^{\cos 2x} 81^{\sin 2x}$ is.......

Find the maximum and minimum values of the function given by $f(x) = |\sin 4x + 3|$.

In triangle $ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$,then $\sin A + \sin B + \sin C =$

If the equation $\cos^4 \theta + \sin^4 \theta + \lambda = 0$ has real solutions for $\theta$,then $\lambda$ lies in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module