Question 145

If $$(\cos \theta + 31^\circ)=\sin47^\circ$$, then what is the value of $$\sin 5\theta $$?

Solution

Given : $$cos(\theta+31^\circ)=sin(47^\circ)$$

=> $$cos(\theta+31^\circ)=sin(90^\circ-43^\circ)$$

Using, $$sin(90^\circ-x)=cos (x)$$

=> $$cos(\theta+31^\circ)=cos(43^\circ)$$

=> $$\theta+31^\circ=43^\circ$$

=> $$\theta=43^\circ-31^\circ$$

=> $$\theta=12^\circ$$

$$\therefore$$ $$sin(5\theta)=sin(5\times12^\circ)$$

= $$sin(60^\circ)=\frac{\sqrt3}{2}$$

=> Ans - (C)

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