if sin theta. cos theta =1/2,then let us write by calculating the value of (sin theta +cos theta)
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Step-by-step explanation:
If sin theta -cos theta =1/2.then find the value of 1/sintheta+cos theta
let use A instead of theta to simplify
sinA - cosA = 1/2
squaring both sides
(sinA - cosA)^2 = (1/2)^2
=> sin^2A + Cos^2A - 2SinAcosA = 1/4
Sin^2A + cos^2A = 1
=> 1 - 2SinACosA = 1/4
=> 2SinACosA = 1- 1/4
=> 2SinACosA = 3/4
(sinA + cosA)^2
= sin^2A + Cos^2A + 2SinAcosA
= 1 + 2SinACosA
= 1 + 3/4
= 7/4
(sinA + cosA)^2 = 7/4
square rooting both sides
SinA + CosA = (root 7) / 2
1/ (Sina + cosA) = 1/(root 7) / 2
= \frac{2}{ \sqrt{7} }=
7
2
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