Question

if sinA-cosA=√3-1/2 then find the value of sinA +cosA​

Answer 1

Answer:

Step-by-step explanation:

SinA-CosA =(√3–1)/2

Squaring both sides

Sin^2A + Cos^2A -2SinACosA = (3+1–2√3)/4 ——eq1

Sin^2A + Cos^2A =1 (Remember this property)

Putting the value of Sin^2A + Cos^2A in eq1

1–2sinACosA = (3+1–2√3)/4

Using basic mathematics you can get the value of SinACosA as √3/4

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Answer 2

SinA - CosA = ($\sqrt{3}$-1) / 2

Squaring both sides

Sin^2 A + Cos^2 A - 2(SinA)(CosA) = (3+1 - 2$\sqrt{3}$) / 4

1 - 2(SinA)(CosA) = 2(2 - $\sqrt{3}$) / 4

1 - (2 - $\sqrt{3}$) / 2 = 2 SinA CosA

(2 - 2 + $\sqrt{3}$) / 2 = 2SinA x CosA = $\sqrt{3}$ / 2             ---------1

(SinA + CosA)^2 = Sin^2 A + Cos^2 A + 2 SinA x CosA

From eq. 1

(SinA + CosA)^2 = 1 + $\sqrt{3}$/2

SinA + CosA = $\sqrt{(2 + \sqrt{3}) / 2}$ : Ans

Hope I helped