Trigonometric Ratio (F.3)

用戶6242

2008-05-24 12:06 am

Simpify the following without a calculator.
1. If tanA=1/2 find the value of (3 sinA- cosA)/ (sinA+3 cosA)
2.Simpify{[sin^2 (90-A) x cos^2A]/ [tan^2(90-A)]} + sin^2(90-A)x cos^2A+cos^2(90-A)

x= times

thx~

回答 (1)

sha wan

2008-05-24 12:13 am

✔ 最佳答案

1. (3 sinA- cosA)/ (sinA+3 cosA)
=(3 tanA- 1)/ (tanA+3) [上下各除以 tanA ]
=(1.5- 1)/ (0.5 + 3)
=0.5/3.5
= 1 / 7
2.
重點：sin(90-A)=cosA, cos(90-A)=sinA

{[sin^2 (90-A) x cos^2A]/ [tan^2(90-A)]} + sin^2(90-A)x cos^2A+cos^2(90-A)
={[cos^2 A cos^2A]/ [tan^2(90-A)]} + cos^2A cos^2A+sin^2A
=cos^4A [cos^2(90-A)] / [sin^2(90-A)] + cos^2A cos^2A+sin^2A
=cos^4A [sin^2A] / [cos^2 A] + cos^2A cos^2A+sin^2A
=cos^2A sin^2A + cos^4A +sin^2A
=cos^2A (sin^2A + cos^2A) +sin^2A
=cos^2A (1) +sin^2A
=1

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