Question 66

If $$\cos \theta = \frac{4}{5}, then \sin^2 \theta \cos \theta + \cos^2 \theta \sin \theta$$ is equal to:

Solution

Given that,

$$\cos \theta = \frac{4}{5}$$

So, $$\sin \theta=\sqrt{1-\cos^2 \theta}=\sqrt{1-(\dfrac{4}{5})^2}=\dfrac{3}{5}$$

Now, substituting the values in $$\sin^2 \theta \cos \theta + \cos^2 \theta \sin \theta$$

$$\Rightarrow (\dfrac{3}{5})^2\times \dfrac{4}{5} +(\dfrac{4}{5})^2\times \dfrac{3}{5}$$

$$\Rightarrow \dfrac{36}{125}+\dfrac{48}{125}$$

$$\Rightarrow \dfrac{84}{125}$$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: