Question

已知θ是锐角,tan(θ+派/4)=3+√2,求cosθ的值

Answer 1

tanθ=tan(θ+派/4-派/4)

=[tan(θ+派/4)-tan(派/4)]/[1+tan(θ+派/4)tan(派/4)]

=(3+√2-1)/(1+3+√2)=(2+√2)/(4++√2)

=(3++√2)/7

(1/cosθ)^2=(tanθ)^2+1=(12+6√2)/49

(cos++√2)^2=49(6-3√2)/36

cosθ=(7/6)*根号(6-3√2)