Question

if sintheta-costheta=1/2 find 1/sintheta+costheta

Answer 1

Answer:

2/√7

Step-by-step explanation:

Given if sintheta - costheta=1/2 find 1/sintheta + costheta

 Let us take sinθ - cosθ = 1/2

squaring both sides we get

    (sinθ - cosθ)^2 = 1/4

sin^2θ + cos^2θ - 2sinθcosθ = 1/4

   1 - 1/4 = 2sinθcosθ

 2sinθcosθ = 3/4

Now (1 / sinθ + cosθ)^2 = 1/ sin^2θ + cos^2θ + 2sinθcosθ

                                     = 1 / 1 + 2sinθcosθ

                                    = 1 / 1 + 3/4

                                  = 1/ 7/4

                             = 4/7

          1/sinθ + cosθ = √4/7

         1/sinθ + cosθ = 2/√7