Question

Cos60=1–2sin²30=2cos²30–1 =cos²30–sin²30, Verify It.

Answer 1

Solve this as shown in the attachment.

Answer 2

cos60° = 1 - 2sin²30° = 2cos²30° - 1 = cos²30° - sin²30° verify it

cos60° = {1/2} [ because cos60° = 1/2 ]
= 1/2

1 - 2sin²30° = 1 - 2 × {1/2}² [ because sin30° = 1/2]
= 1 - 2 × 1/4 = 1 - 1/2 = 1/2

2cos²30° - 1 = 2 × {√3/2}² - 1 [ because cos30°=√3/2]
= 2 × 3/4 - 1 = 3/2 - 1 = 1/2

cos²30° - sin²30° = {√3/2}² - {1/2}²
= 3/4 - 1/4 = 2/4 = 1/2

here it is clear that, cos60° = 1 - 2sin²30° = 2cos²30° - 1 = cos²30° - sin²30°