Question

If sinθ + cosθ = 7/5, then sinθ cosθ is?
1. 11/25
2. 12/25
3. 13/25
4. 14/25
5. None of these

Answer 1

Correct Answer - Option 2 : 12/25

Concept:

sin² x + cos² x = 1

Calculation:

Given: sinθ + cosθ = 7/5 

By, squaring both sides of the above equation we get,

⇒ (sinθ + cosθ)² = 49/25

⇒ sinθ² + cosθ² + 2sinθ.cosθ = 49/25

As we know that, sin2 x + cos2 x = 1

⇒ 1 + 2sinθcosθ = 49/25

⇒ 2sinθcosθ = 24/25

∴ sinθcosθ = 12/25