What is the value of 2 sin 15° cos 15° - 4 sin³ 15° cos 15°?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. √3/4.
Given:
2 sin 15° cos 15°-4 sin³ 15° cos 15°
Formulae Used:
Sin 2A= 2sinA cosA
Cos 2A = 1-2Sin²A
Calculation:
⇒ 2 sin 15° cos 15° - 4 sin³ 15° cos 15°
⇒ sin 30°- 2sin215° sin30°
⇒ sin 30°(1 - 2 sin215°)
⇒ sin 30° cos 30°
⇒ 1/2 × √3/2
⇒√3/4