NTA Abhyas JEE Main2020MathematicsTrigonometric Ratios & IdentitiesPractice
If sin 2 β is the geometric mean between sin α and cos α , then cos 4 β is equal to
Options
- A2 sin 2 π 4 - α
- B2 cos 2 π 4 - α
- C2 cos 2 π 2 + α
- D2 sin 2 π 4 + α
Correct answer
A. 2 sin 2 π 4 - α
Step-by-step solution
sin 2 2 β = sin α cos α cos 4 β = 1 - 2 sin 2 2 β = sin 2 α + cos 2 α - 2 sin α cos α = sin α - cos α 2 = 2 sin α · 1 2 - cos α 1 2 2 = 2 sin α cos π 4 - cos α sin π 4 2 = 2 sin α - π 4 2 = 2 sin 2 π 4 - α