Question

sec50°sin40°+cos40°cosec50°=2

Answer 1

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Answer 2

Answer:

We know that sin(90° - θ) = cosθ and cos(90°− θ)=sinθ

∴ sin40° = sin(90°− 50°) = cos50°

and cos40° = cos(90°− 50°) = sin50°

∴ LHS = sec50°sin40°+cos40°cosec50°

          = sec50°cos50° + sin50°cosec50°

          = (1/cos50°) × cos50° + sin50° × (1/sin50°)   ----- (∵ secθ = 1/cosθ and cosecθ = 1/sinθ)

         = 1 + 1

        = 2

       = RHS

∴ sec50°sin40°+cos40°cosec50°=2

Step-by-step explanation: