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# maths question

1.cos30度xcos45度+sin60度xsin45度

2. cos^2 45度xsin30度

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tan^2 60度

3. tan60度 = 開方8xcos45度

_______

sin(acute angle/3+35度)

4.BCDE is a triangle and ABC is a straight line. If Ad is 20cm,AE =10x開方2and ADE=60度,find the lenght of CD and cx

### 1 Answer

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(I omitted the degree notation)

sqrt. denotes square root.

(1)

(cos 30)(cos 45)+(sin 60)(sin 45)

=(2 sqrt.)/2[2 cos 30]

=(2 sqrt.)cos 30

=(2 sqrt.)(3 sqrt./2)

=6 sqrt./2

(2)

(cos²45)(sin 30)/tan²60

=(2 sqrt./2)²(1/2)/(3 sqrt.)²

=(1/2)(1/2)/3

=1/12

(3)

tan 60/sin (θ/3+35)=8 sqrt. cos 45

3 sqrt./sin (θ/3+35)=2(2 sqrt.)(2 sqrt.)/2

3 sqrt./sin (θ/3+35)=2

sin (θ/3+35)=3 sqrt./2

Because θ is an acute angle, therefore there is only one solution for θ/3+35

θ/3+35=60

θ/3=25

θ=75

(4)

Is there a figure?

I think it is not showing clearly.

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