If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.

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KollegeApply · Accepted Answer

If sin$\theta$ – cos$\theta$ = 0, then the value of (sin4$\theta$ + cos4$\theta$) is underlinebb($\frac{1}{2}$). Explanation: Given, sin $\theta$ – cos $\theta$ = 0 $\Rightarrow$ sin $\theta$ = cos $\theta$ $\Rightarrow$ sintheta/costheta = 1 $\Rightarrow$ tan $\theta$ = 1 ...`[∵ tan theta = sintheta/costheta "and" tan 45^circ = 1]` $\Rightarrow$ tan $\theta$ = tan $45^\circ$ $\therefore$ $\theta$ = $45^\circ$ Now, sin4$\theta$ + cos4$\theta$ = sin$445^\circ$ + cos$445^\circ$ = `(1/sqrt(2))^4 + (1/sqrt(2))^4 ...[∵ sin 45^circ = cos 45^circ = 1/sqrt(2)] = $\frac{1}{4}$ + $\frac{1}{4}$ = $\frac{2}{4}$ = $\frac{1}{2}$`

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