Question

(cos θ + sin θ)2 + (cos θ – sin θ)2 is equal to

Answer 1

Answer:

This is equal to 4

Answer 2

Let : For convenience ,I'll take theta as "x"

To find : Value of ,(cos θ + sin θ)² + (cos θ – sin θ)²

As I have taken theta = x ,

( cos x + sin x )² + ( cosx - sin x)²

Identity used :

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² - 2ab
• sin²x + cos²x = 1

Solution :

➠ ( cos x + sin x )² + ( cosx - sin x)²

➠ { (cos x)² + (sin x)² + 2(cos x)(sin x) } + { (cos x)² + (sin x)² - 2(cos x)(sin x) }

➠ cos²x + sin²x + 2(cos x)(sin x) + cos²x + sin²x - 2(cos x)(sin x)

➠ (cos²x + sin²x) + (cos²x + sin²x) + 2(cos x)(sin x) + - 2(cos x)(sin x)

➠ (cos²x + sin²x) + (cos²x + sin²x)

➠ 1 + 1

➠ 2

ANSWER : (cos θ + sin θ)² + (cos θ – sin θ)² = 2