Question

If sinA=1/2 then find sinA +cos A
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Answer 1

Explanation:

Given sinA – cosA = 1/2 squaring on both the sides, we get (sinA – cosA)2 = (1/2)2 ⇒ sin2A + cos2A – 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 .

Answer 2

Given that,

`\sin A = \frac 12\\\\ \implies \sin^2 A = \frac 14\\\\\ \implies 1-\cos^2 A = \frac 14\\\\\ \implies \cos^2 A = 1 - \frac 14 = \frac 34\\\\\ \implies \cos A = \pm \frac{\sqrt 3}2\\\\\text{Case 1:}\\\\\sin A + \cos A = \frac 12 + \frac{\sqrt 3}2 = \frac{1 + \sqrt 3}2\\\\\text{Case 2:}\\\\\sin A + \cos A = \frac 12 +\left(- \frac{\sqrt 3}2\right) = \frac 12 - \frac{\sqrt 3}2=\frac{1 - \sqrt 3}2`