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

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(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

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

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(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:

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