Math, asked by ishwargupta987, 11 months ago

(sinA+cosA)²+(sinA-cosA)²=

Answers

Answered by Anonymous
2

Step-by-step explanation:

2sin^(a) + 2cos^(a) = 2

Answered by HappiestWriter012
21

To find :

The value of (sinA+cosA)²+(sinA-cosA)²

Solution

⇒(sinA+cosA)²+(sinA-cosA)²

⇒ sin²A + cos²A + 2sinAcosA + sin²A + cos²A - 2sinAcosA

⇒2sin²A + 2 cos²A

⇒ 2sin²A + 2 ( 1- sin²A)

⇒2 ( sin²A - sin²A + 1)

⇒ 2(1)

⇒ 2

Alternative method :

We know

(a+b)² + (a-b)² = 2(a²+b²)

So, (sinA+cosA)²+(sinA-cosA)² = 2(sin²A + cos²A) = 2

Since, sin²A + cos²A = 1.

Similar questions