Question

If sec 2A = cosec 8A, where 0 < 2A < π/2, then what is the value of sin5A.
1. (1/2)
2. √3/2
3. 0
4. (1/√2)

Answer 1

Correct Answer - Option 4 : (1/√2)

Given

sec 2A = cosec 8A

Formula used

cosec (90° - A) = sec A

Calculation

sec 2A = cosec 8A

cosec(90° - 2A) = cosec8A

⇒ 90° - 2A = 8A

⇒ 90° = 8A + 2A

⇒ 90 = 10A

A = 9 

sin5(9) = sin 45° 

⇒ (1/√2)

∴ The value of sin 5A is (1/√2)