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Question

If sinA - cos A = 1/2, then find the value of 1/(sinA+cosA)

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Solution

Given sinA – cosA = 1/2
squaring on both the sides, we get
(sinA – cosA)^2 = (1/2)^2

⇒ (^2sinA) + (cosA)^2 – 2sinA cosA = 1/4
⇒ 1 – 2sinA cosA = 1/4
⇒ 1 – (1/4) = 2sinA cosA
⇒ 2sinA cosA = 3/4
∴ sinA cosA = 3/8 → (1)
(sinA + cosA)2 = (sinA – cosA)^2 + 4sinA cosA
= (1/2)^2 + 4(3/8)
= (1/4) + (3/2) = 7/4
(sinA + cosA) = √(7/4) = (√7)/2

So 1÷(sinA +cos A)
=2÷√7

LIKE IF SATISFIED

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