Question 63

Find the value of $$\sin (60 + \theta) - \cos(30 - \theta)$$.

Solution

$$\sin(60+\theta)-\cos(30-\theta)=\sin60\cos\theta\ +\cos60\sin\theta\ -\left(\cos30\cos\theta\ +\sin30\sin\theta\ \right)$$

$$=\frac{\sqrt{3}}{2}\cos\theta\ +\frac{1}{2}\sin\theta\ -\left(\frac{\sqrt{3}}{2}\cos\theta\ +\frac{1}{2}\sin\theta\ \right)$$

$$=\frac{\sqrt{3}}{2}\cos\theta\ +\frac{1}{2}\sin\theta\ -\frac{\sqrt{3}}{2}\cos\theta\ -\frac{1}{2}\sin\theta\ $$

$$=0$$

Hence, the correct answer is Option C


Create a FREE account and get:

  • Free SSC Study Material - 18000 Questions
  • 230+ SSC previous papers with solutions PDF
  • 100+ SSC Online Tests for Free

cracku

Boost your Prep!

Download App