Question

If sinB = 5 cosB/12, find the value of tan2B.

1. 60/13
2. 120/119
3. 57/55
4. 140/137

Answer 1

Correct Answer - Option 2 : 120/119

Given:

sinB  = 5 cosB/12

Concepts used:

tanB = sinB/cosB

tanB = P/B

→ P = Perpendicular, B = Base, H = Hypotenuse

Calculation:

sinB = 5 cosB/12

⇒ sinB/cosB = 5/12

⇒ tanB = 5/12

tan2B = 2tanB/(1 – tan²B)

⇒ tan2B = 2 × (5/12)/{1 – (5/12)²}

⇒ tan2B = 120/119

∴ tan2B is equal to 120/119.