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8. Introduction to Trigonometry
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यदि $\sin \theta-\cos \theta=0$ है, तो $\left(\sin ^{4} \theta+\cos ^{4} \theta\right)$ का मान है:
A
$\frac{1}{2}$
B
$\frac{3}{4}$
C
$1$
D
$\frac{1}{4}$
Solution
Given, $\sin \theta-\cos \theta=0$
$\sin \theta=\cos \theta \Rightarrow \frac{\sin \theta}{\cos \theta}=1$
$\tan \theta=1$ $\left[\because \tan \theta=\frac{\sin \theta}{\cos \theta}\right.$ and $\left.\tan 45^{\circ}=1\right]$
$\tan \theta=\tan 45^{\circ}$
$\theta=45^{\circ}$
Now, $\sin ^{4} \theta+\cos ^{4} \theta=\sin ^{4} 45^{\circ}+\cos ^{4} 45^{\circ}$
$=\left(\frac{1}{\sqrt{2}}\right)^{4}+\left(\frac{1}{\sqrt{2}}\right)^{4}$ $\left[\because \sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$
$=\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$
Standard 10
Mathematics
