Question

Cos theta+sintheta=√2costheta then cos theta-sintheta is equal to

Answer 1

Answer:-

"Theta" is taken as "A".

Given:

Cos A + Sin A = √2Cos A -- equation (1)

Squaring both sides we get,

→ (Cos A + Sin A)² = 2 Cos²A

→ Cos² A + Sin² A + 2*Sin A*Cos A = 2 Cos² A

[(a + b)² = a² + b² + 2ab]

→ 2* Sin A* Cos A = 2 Cos² A - Cos² A - Sin² A

→ 2 Sin A Cos A = Cos² A - Sin² A

→ 2 Sin A Cos A = (Cos A + Sin A)(Cos A - Sin A)

[(a + b)(a - b) = a² - b² ]

→ 2 Sin A Cos A = (√2 Cos A)(Cos A - Sin A) [ from equation (1)]

→ Cos A - Sin A = 2 Sin A Cos A/√2 Cos A

→ Cos A - Sin A = √2 Sin A