Question

If sin α + cos α = p, then what is cos² (2α) equal to?
1. p²
2. p² - 1
3. p²(2- p²)
4. p² + 1
5. None of these

Answer 1

Correct Answer - Option 3 : p²(2- p²)

Concept:

sin² x + cos² x = 1

sin 2x = 2 sin x cos x

Calculation:

Given: sin α + cos α = p

By squaring both the sides, we get

⇒ sin² α + cos² α + 2 sin α cos α = p²

As we know that, sin² x + cos² x = 1 and sin 2x = 2 sin x cos x

⇒ 1 + sin 2α = p² ⇒ sin 2α = p² – 1

⇒ cos² 2α = 1 – sin² 2α = 1 – (p² – 1)²

⇒ cos² 2α = p² (2 – p²)