Question

any one please tell me the answer to the above question in the picture​

Answer 1

Answer:

2 is the answer for this question

Step-by-step explanation:

Given that,

(sinθ + cosθ)² + (cosθ - sinθ)²

Using the identity

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

[ sin²θ + cos²θ + 2sinθ.cosθ ] + [cos²θ + sin²θ - 2sinθ.cosθ]

1 + 2sinθ.cosθ + 1 - 2sinθ.cosθ        [We know, sin²θ + cos²θ = 1]

1 +  1 + [ 2sinθ.cosθ - 2sinθ.cosθ ]

1 + 1 +0

2

Therefore (sinθ + cosθ)² + (cosθ - sinθ)² = 2