Question

If 3cosθ - 4sinθ = 1/2, then find the value (4cosθ + 3 sinθ).
1. √11
2. (3/2)√11
3. √10
4. 2 

Answer 1

Correct Answer - Option 2 : (3/2)√11

3cosθ - 4sinθ = 1/2 

Formula used :

If, ax + by = m, ay - bx = n 

then, (a2 + b2)(x2 + y2) = m2 + n2

Calculations :

Let, 3sinθ + 4cosθ be x 

Now, 

3cosθ - 4sinθ = 1/2     ...1)

3sinθ + 4cosθ = x     ...2) 

Comparing with above given formula 

(32 + 42) (sin2θ + cos2θ) = (1/2)2 + x2 

⇒ 25 × 1 = (1/4) + x2 

⇒ x2 = 25 - (1/4)

⇒ x = √(99/4)

⇒ x = (3/2)√11

∴ The value of (4cosθ + 3sinθ) is (3/2)√11.