Question

If 3sin$\theta$ + 5 cos$\theta$ = 5 then value of sin$\theta$ - 3 cos$\theta$ is equal to

• A. 5
• B. 3
• C. 4
• D. 1

Answer 1

The correct option is B

3

3sin$\theta$ = 5(1 - cos$\theta$) = 5 × $2si{n}^2$ $\frac{\theta }{2}$

⇒ tan $\frac{\theta }{2}$ = $\frac{3}{5}$

Now 5sin$\theta$ - 3cos$\theta$ = $\frac{5\times 2tan\frac{\theta }{2}}{1+ta{n}^2\frac{\theta }{2}}$ - 3 $\frac{(1-ta{n}^2\frac{\theta }{2})}{1+ta{n}^2\frac{\theta }{2}}$

= 5 × $\frac{2\times \frac{3}{5}}{1+\frac{9}{5}}$ - 3 × $\frac{1-\frac{9}{25}}{1+\frac{9}{25}}$ = 3