Question

(sin theta + cos theta)^2 + (sin theta - cos theta)^2?​

Answer 1

See below. Explanation: Left Side =sin2θ+2sinθcosθ+cos2θ+sin2θ−2sinθ cosθ+cos2θ. =(sin2θ+cos2θ)+(sin2θ+cos2θ)

Answer 2

Solution:

( sin θ + cos θ)^2 + ( sin θ - cos θ)^2

= (sin θ + cos θ)^2 + (sin θ - cos θ)^2

= (sin^2 θ + 2sin θ cos θ + cos^2 θ) + (sin^2 θ - 2sin θ cos θ + cos^2 θ)

= (sin^2 θ + cos^2 θ) + 2sin θ cos θ) + (sin^2 θ + cos^2 θ) - 2sin θ cos θ)

= (1 + 2sin θ cos θ) + (1 - 2sin θ cos θ)

= 2

Hope this would help