Q. Find tan θ, if sin (60°+θ)= cos θ. Ans. : 2-√3
Q 2. If A, B and C are angles of triangle, prove that (tanA/2 tanB/2)+ (tanB/2 tanC/2)+ (tanC/2 tanA/2)=1 Thanks!
M 2 maths Trigonometric 40 pts
2011-02-25 6:31 am
回答 (1)
2011-02-26 1:41 am
✔ 最佳答案
1) sin(60°+θ) = cos θsin60° cosθ + cos60° sinθ = cosθsin60° + cos60° tanθ = 1√3/2 + (1/2)tanθ = 1tanθ = 2(1 - √3/2) = 2 - √3 2) tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2= tan A/2 tan B/2 + (tan C/2) (tan B/2 + tan A/2)= tan A/2 tan B/2 + (tan C/2) [tan (B/2 + A/2)](1 - tan B/2 tan A/2)= tan A/2 tan B/2 + (tan C/2) [tan (π/2 - C/2)](1 - tan B/2 tan A/2)= tan A/2 tan B/2 + (1 - tan B/2 tan A/2)= 1
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