Завдання на фото алгебра

Объяснение:

1) (1+ ctgβ)²+ (1 - ctgβ )²=1+2ctgβ+ctg²β+1-2ctgβ+ctg²β=

=2+2ctg²β=2(1+ctg²β)=1/sin²β;

2)

�

�

�

+

�

�

�

�

1

+

�

�

�

�

=

�

�

�

(

1

+

�

�

�

�

)

+

�

�

�

�

1

+

�

�

�

�

=

�

�

�

+

�

�

�

2

�

�

�

�

�

+

�

�

�

�

1

+

�

�

�

�

=

�

�

�

�

+

�

�

�

2

�

+

�

�

�

2

�

�

�

�

�

∗

∗

1

1

+

�

�

�

�

=

1

+

�

�

�

�

�

�

�

�

∗

1

1

+

�

�

�

�

=

1

�

�

�

�

;

tgx+

1+sinx

cosx

=

1+sinx

tgx(1+sinx)+cosx

=

1+sinx

tgx+

cosx

sin

2

x

+cosx

=

cosx

sinx+sin

2

x+cos

2

x

∗

∗

1+sinx

1

=

cosx

1+sinx

∗

1+sinx

1

=

cosx

1

;

3)

�

�

�

�

1

−

�

�

�

�

+

1

−

�

�

�

�

�

�

�

�

=

�

�

�

2

�

+

1

−

2

�

�

�

�

+

�

�

�

2

�

(

1

−

�

�

�

�

)

�

�

�

�

=

2

(

1

−

�

�

�

�

)

(

1

−

�

�

�

�

)

�

�

�

�

=

2

�

�

�

�

;

1−sinβ

cosβ

+

cosβ

1−sinβ

=

(1−sinβ)cosβ

cos

2

β+1−2sinβ+sin

2

β

=

(1−sinβ)cosβ

2(1−sinβ)

=

cosβ

2

;

4)

1

+

�

�

�

1

+

�

�

�

�

=

�

�

�

�

+

�

�

�

�

�

�

�

�

∗

�

�

�

�

�

�

�

�

+

�

�

�

�

=

�

�

�

�

�

�

�

�

=

�

�

�

.

1+ctgα

1+tgα

=

cosα

cosα+sinα

∗

sinα+cosα

sinα

=

cosα

sinα

=tgα.