Ответ:

1)

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80

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40

=

2

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40

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40

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40

=

2

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�

40

cos40

sin80

=

cos40

2sin40cos40

=2sin40

2)

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4

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+

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2

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∗

2

=

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4

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+

2

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2

�

cos4β+sin2β∗2=cos4β+2sin2β

3)

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6

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+

2

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3

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∗

2

=

�

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6

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+

4

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3

�

cos6α+2sin3α∗2=cos6α+4sin3α

4)

1

+

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2

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(

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+

�

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)

2

=

1

+

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2

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2

+

2

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+

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2

=

1

+

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2

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1

+

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2

�

=

1

(sinα+cosα)

2

1+sin2α

=

sinα

2

+2sinαcosα+cosα

2

1+sin2α

=

1+sin2α

1+sin2α

=1

5)

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∗

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2

−

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2

)

=

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2

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sinαcosα∗(cosα

2

−sina

2

)=sinαcosαcos2α

6)

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4

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�

4

−

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4

=

2

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2

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2

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(

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2

−

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2

)

∗

(

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2

+

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2

)

=

2

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2

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2

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2

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∗

1

=

2

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2

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2

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2

�

=

2

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2

�

cosα

4

−sinα

4

sin4α

=

(cosα

2

−sinα

2

)∗(cosα

2

+sinα

2

)

2sin2αcos2α

=

cos2α∗1

2sin2αcos2α

=

cos2α

2sin2αcos2α

=2sin2α

7)

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(

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4

−

�

)

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−

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)

=

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4

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−

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4

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∗

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4

)

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+

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)

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)

=

(

2

2

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−

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2

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∗

(

2

2

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∗

2

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)

=

(

2

∗

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2

−

2

∗

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2

)

∗

(

2

∗

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2

+

2

∗

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2

)

=

2

∗

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−

2

∗

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2

∗

sin(

4

π

−α)cos(

4

π

−α)=(sin(

4

π

)cosα−cos(

4

π

)sinα)∗(cos(

4

π

)cosα+sib(

4

π

)sinα)=(

2

2

∗cosα−

2

2

∗sinα)∗(

2

2

∗cosα∗

2

2

∗sinα)=(

2

2

∗cosα

−

2

2

∗sinα

)∗(

2

2

∗cosα

+

2

2

∗sinα

)=

2

2

∗cosα−

2

∗sinα

∗

∗

2

∗

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+

2

∗

�

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�

�

2

=

(

2

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−

2

∗

�

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�

)

∗

(

2

∗

�

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�

�

+

2

∗

�

�

�

�

)

4

=

2

�

�

�

�

2

−

2

�

�

�

�

2

4

=

2

(

�

�

�

�

2

−

�

�

�

�

2

)

4

=

�

�

�

2

�

2

∗

2

2

∗cosα+

2

∗sinα

=

4

(

2

cosα−

2

∗sinα)∗(

2

∗cosα+

2

∗sinα)

=

4

2cosα

2

−2sinα

2

=

4

2(cosα

2

−sinα

2

)

=

2

cos2α