The value of [√(3) + 2Sin P/1 – 2 Cos P]3 + [1 + 2Cos P/ √(3) – 2Sin P]3 is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 0
| Understanding | Application |
| We will use trigonometric identities to solve the given question. |
We have the equation given as ⇒ [√(3) + 2Sin P/ 1 – 2 Cos P]3 + [1 + 2Cos P/ √(3) – 2Sin P]3 We will divide each term by '2' to convert the given equation into the form. ⇒ [√(3 / 2) + Sin P) / 1 / 2 – Cos P]3 + [1 / 2 + Cos P/ √(3 / 2) – Sin P]3 Here we will use identities as Sin A + Sin B = Sin(A + B / 2) + Cos(A - B / 2) We would get ⇒ [(Sin π / 3 + Sin P) / (Cos π / 3 – Cos P)]3 + [(Cos π / 3 + Cos P) / (Sin π / 3 – Sin P)]3 ⇒ [2Sin (π / 3 + P) / 2 × Cos (π / 3 - P) / 2 / -2Sin (π / 3 + P) / 2 × Sin(π / 3 + P) / 2]3 + [2Cos (π / 3 + P) / 2 × Cos (π / 3 - P) / 2 / 2Cos (π / 3 + P / 2) × Cos(π / 3 + P / 2)]3 ⇒ - Cot3(π / 3 - P) / 2 + Cot3(π / 3 - P) / 2 ⇒ 0 |