(sinA+cosA)²+(sinA-cosA)²=
Answers
Answered by
2
Step-by-step explanation:
2sin^(a) + 2cos^(a) = 2
Answered by
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.
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