If A = 2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) then the value of 3α such that cosα = √(3+A/5+A) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 135o
| Understanding | Application |
| We will use basic algebraic identities to convert trigonometric functions to simple forms. |
Given that, ⇒ A = 2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) We know that, (a3 + b3 = (a + b)3 - 3ab(a + b)) and, (a2 + b2 = (a + b)2 - 2ab) ⇒ A = 2{(Sin2 θ + Cos2 θ)3 - 3Sin2 θ × Cos2 θ(Sin2 θ + Cos2 θ)} - 3{(Sin2 θ + Cos2 θ) - 2 × Sin2 θ × Cos2 θ} ⇒ A = 2{1 - 3 × Sin2 θ × Cos2 θ} - 3{1 - 2 × Sin2 θ × Cos2 θ} ⇒ A = -1 ⇒Cosα = √(3+A/5+A) ⇒Cosα = √(2 / 4) ⇒ α = 45° ⇒ 3 × α = 3 × 45o = 135o |