Question 62

If $$sin^2\theta-cos^2\theta=\frac{1}{4}$$, then the value of $$sin^4\theta-cos^4\theta$$ is

Solution

Given : $$sin^2\theta-cos^2\theta=\frac{1}{4}$$ -------(i)

To find : $$sin^4\theta-cos^4\theta$$

= $$(sin^2\theta-cos^2\theta)(sin^2\theta+cos^2\theta)$$

$$\because$$ $$(sin^2\theta+cos^2\theta=1)$$ ---------(ii)

Substituting values from equations (i) and (ii), we get :

= $$(\frac{1}{4}) \times 1 = \frac{1}{4}$$

=> Ans - (B)

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