Question

sin theta.cos theta = 1/2 then theta is ​

Answer 1

Answer:

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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Answer 2

Answer:

x = 45°

Step-by-step explanation:

sin x . cos x = 1/2 tan x

sin x . cos x = 1/2 (sinx/cos x)

cos²x = 1/2

cos x = 1/√2

cos x = cos 45°

x = 45°

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