Question

三角函数计算：若sinθ+cosθ=√2 则tan(θ+π/3)=?

Answer 1

sinθ+cosθ=√2

平方得1+2sinθcosθ=2

sinθcosθ=1/2 ①

sin²θ+cos²θ=1 ②

①/②得

(sinθcosθ)/(sin²θ+cos²θ)=1/2

左边分子分母同时除以cos²θ得tanθ/(tan²θ+1)=1/2

从而得到tanθ=1

tan(θ+π/3)

=[tanθ+tan(π/3)]/[1-tanθtan(π/3)]

=(1+√3)/(1-√3)

=-2-√3