Question

cos + sin =  √2 cos तो cos - sin =  √2 sin सिध्द करिये​

Answer 1

Answer:-

Given:

Cos A + sin A = (√2) * Cos A

On squaring both sides we get,

→ (Cos A + sin A)² = (√2)² * cos² A

Using the formula (a + b)² = a² + b² + 2ab in LHS we get,

→ cos² A + sin² A + 2 sin A Cos A = 2 cos² A

→ 2 sin A Cos A = 2 cos² A - cos² A - sin² A

→ 2 sin A Cos A = cos² A - sin² A

Using the formula (a² - b²) = (a + b) * (a - b) in RHS we get,

→ 2 sin A cos A = (Cos A + sin A) * (Cos A - sin A)

Putting the value of (Cos A + sin A) as √2 * Cos A in RHS we get,

→ 2 sin A Cos A = (√2 * Cos A) * (Cos A - sin A)

→ (2 sin A * Cos A) / (√2 * Cos A) = Cos A - sin A

→ √2 * sin A = Cos A - sin A

Hence, Proved.