If sinθ+cosθ=3,sinθ+cosθ=3,sinθ+cosθ=3, simplify tanθ+cotθ.tanθ+cotθ.


Answer:

11

Step by Step Explanation:
  1. It is given that
    sinθ+cosθ=3(sinθ+cosθ)2=3  ...........................[ On squaring both sides. ]sin2θ+cos2θ+2sinθcosθ=3  ..........[ Using identity: (a+b)2=a2+b2+2ab]1+2sinθcosθ=3  .............................[ Using identity: sin2θ+cos2θ=1]sinθcosθ=312sinθcosθ=1
  2. Now, we can re-write expression tanθ+cotθ as follows.
    S=tanθ+cotθS=sinθcosθ+cosθsinθS=sin2θ+cos2θsinθcosθS=1sinθcosθS=11=1

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