Question

SinA - cosA= 1/2 to find 1/(sinA + CosA)

Answer 1

If sinA-cosA=1/2 .then find 1/sinA+cosA

1/(sinA + cosA) = 2/√7

Step-by-step explanation:

Given that sin(A) - cos(A) = 1/2

Square both sides, you get

(sin(A) - cos(A))^2 = 1/4

sin^2(A) + cos^(A) - 2sin(A)cos(A) = 1/4

Sin^2(A) + cos^2(A) = 1.

Substituting in above equation

2Sin(A)Cos(A) = 1 - 1/4 = 3/4

Now Take the equation

(Sin(A) + Cos(A))^2 = sin^2(A) + cos^(A) + 2sin(A)cos(A)

= 1 + 2Sin(A)Cos(A) = 1 + 3/4 = 7/4

Apply square root both sides, you get

Sin(A) + Cos(A) = √7/2

Hence 1/(Sin(A) + Cos(A)) = 2/√7

Hope it helps

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