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Question 142
If $$\sin \theta - \cos \theta = 0, 0^\circ < \theta < 90^\circ$$, then the value of $$\sin^4 \theta + \cos^4 \theta$$ is:
Solution
Given,
$$sin\theta-cos\theta=0$$
$$sin\theta=cos\theta$$
$$sin\theta=sin(90-\theta)$$
$$\theta=90-\theta$$
$$\theta+\theta=90$$
$$2\theta=90$$
$$\theta=45$$
$$sin^4\theta+cos^4\theta$$
$$sin^4(45)+cos^4(45)$$
$$(\dfrac{1}{\sqrt2})^4+(\dfrac{1}{\sqrt2}^4)$$
$$\dfrac{1}{4}+\dfrac{1}{4}$$
$$\dfrac{1}{2}$$
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