Question

If 3sinθ + 5cosθ = 5, then the value of 5sinθ – 3cosθ is equal to

• A. 5
• B. 3
• C. 4
• D. None of these

Answer 1

Answer: (B)

3

Answer 2

3sinθ = 5(1 – cosθ) = 5 × 2sin²θ/2

⇒tanθ/2 = 3/5

5sinθ – 3cosθ = $5 \times \frac{2\tan\frac{\theta}{2}}{1 + \tan^{2}\frac{\theta}{2}} - 3\frac{\left( 1 - \tan^{2}\frac{\theta}{2} \right)}{1 + \tan^{2}\frac{\theta}{2}}$

= $5 \times \frac{2 \times \frac{3}{5}}{1 + \frac{9}{25}} - \frac{3 \times \left( 1 - \frac{9}{25} \right)}{1 + \frac{9}{25}} = 3$