Question

Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2

options are
1
2
sin2 Θ
cos2 Θ

Answer 1

2 is the right answer.

Explanation:

(sin∅-cos∅)²+(sin∅+cos∅)² in this expression we will open the brackets first by squaring the expressions given inside.

(sin²∅+cos²∅-2sin∅cos∅)+(sin²∅+cos²∅+2sin∅cos∅)

Since (a+b)² = a²+b²+2ab and (a-b)² = a²+b²-2ab

⇒(1-2sin∅cos∅) + (1+2sin∅cos∅)

Since (sin²∅+cos²∅) =1

⇒ 1-2sin∅cos∅+1+2sin∅cos∅

⇒ 1+1

⇒ 2

Therefore the option 2 is right answer.