F3 Trigonometry(2)

銀雞

2011-05-16 7:43 am

1a)express cosθ+3sinθ/2sinθ-cosθ in terms of tanθ
b)if tanθ=3,find the value of cosθ+3sinθ/2sinθ-cosθ

2.prove that cos^2θ-sin^2θ=2cos^2θ-1

3.prove that cos^4θ-sin^4θ=2cos^2θ-1

回答 (1)

螞蟻雄兵

2011-05-16 8:23 am

✔ 最佳答案

1a)express (Cosθ+3Sinθ)/(2Sinθ－Cosθ) in terms of Tanθ
Sol
(Cosθ+3Sinθ)/(2Sinθ－Cosθ)
=(Cosθ/Cosθ+3Sinθ/Cosθ)/(2Sinθ/Cosθ－Cosθ/Cosθ)
=(1+3Tanθ)/(2Tanθ－1)

b)if Tanθ=3，find thevalue of (Cosθ+3Sinθ)/(2Sinθ－Cosθ)
Sol
(Cosθ+3Sinθ)/(2Sinθ－Cosθ)
=(1+3Tanθ)/(2Tanθ－1)
=(1+3*3)/(2*3－1)
=2

2.prove that Cos^2 θ－Sin^2 θ=2Cos^2 θ－1
Sol
Cos^2 θ－Sin^2 θ
=Cos^2 θ－(1－Cos^2 θ)
=2Cos^2θ－1

3.prove that Cos^4 θ－Sin^4 θ=2Cos^2 θ－1
Sol
Cos^4 θ－Sin^4 θ
=(Cos^2 θ－Sin^2 θ)(Cos^2θ+Sin^2 θ)
=Cos^2 θ－Sin^2 θ
=2Cos^2θ－1

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