1.Simplify tanθcosθ + 4sin(180° - θ)
2.Prove the identity sin^4 θ - cos^4 θ = 2sin^2 θ -1
3.Consider y = ksin(θ - 20°) where 0° < θ < 360° and k > 0.
(a) Find the value of k.
(b) Find the minimum value of y and the corresponding value of θ.
F4 math problems
2007-07-17 5:50 am
回答 (1)
2007-07-17 8:14 am
✔ 最佳答案
1. Simplify:tanθcosθ + 4sin(180° - θ)
=(sinθ/cosθ)*cosθ + 4sinθ
=sinθ+4sinθ
=5sinθ
2. Proof:
LHS=sin^4 θ - cos^4 θ
=(sin^2 θ + cos^2 θ)(sin^2 θ - cos^2 θ)
=(1)(sin^2 θ - cos^2 θ)
=sin^2 θ - cos^2 θ
=sin^2 θ + sin^2 θ - cos^2 θ - sin^2 θ
=2sin^2 θ - (sin^2 θ + cos^2 θ)
=2sin^2 θ - 1
=RHS
收錄日期: 2021-04-18 22:40:24
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