Question 68

If $$\cos^2 \theta + cos^4 \theta = 1$$, then the value of $$\sin \theta + \sin^2 \theta$$ is:

Solution

Given,

$$\cos^2 \theta + cos^4 \theta = 1$$

$$=$$> $$\cos^2\theta+\cos^4\theta=\sin^2\theta\ +\cos^2\theta\ $$

$$=$$> $$\cos^4\theta=\sin^2\theta\ $$

$$=$$> $$\sin\theta\ =\cos^2\theta\ $$

$$\therefore\ $$ $$\sin\theta+\sin^2\theta=\cos^2\theta\ +\left(\cos^2\theta\right)^2=\cos^2\theta\ +\cos^4\theta=1$$

Hence, the correct answer is Option C

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