If sinθ+cosθ=√3,sinθ+cosθ=√3,sinθ+cosθ=√3, simplify tanθ+cotθ.tanθ+cotθ.
Answer:
11
- 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=3−12⟹sinθcosθ=1 - Now, we can re-write expression tanθ+cotθ as follows.
S=tanθ+cotθ⟹S=sinθcosθ+cosθsinθ⟹S=sin2θ+cos2θsinθcosθ⟹S=1sinθcosθ⟹S=11=1