Math, asked by vijithakoduru, 8 months ago

if a+b+c=180 then cosa+cosb-cosc=

Answers

Answered by Mahi2605
0

Answer:

As

A

,

B

and

C

are angles of a triangle, we have

A

+

B

+

C

=

180

and

A

+

B

=

180

C

or

A

+

B

2

=

90

C

2

Hence

cos

A

+

cos

B

+

cos

C

=

2

cos

(

A

+

B

2

)

cos

(

A

B

2

)

+

1

2

sin

2

(

C

2

)

1

=

2

cos

(

90

C

2

)

cos

(

A

B

2

)

+

1

2

sin

2

(

C

2

)

=

2

sin

(

C

2

)

cos

(

A

B

2

)

+

1

2

sin

2

(

C

2

)

=

2

sin

(

C

2

)

(

cos

(

A

B

2

)

sin

(

C

2

)

)

+

1

=

2

sin

(

C

2

)

(

cos

(

A

B

2

)

cos

(

A

+

B

2

)

)

+

1

=

2

sin

(

C

2

)

(

2

sin

(

A

2

)

sin

(

B

2

)

)

+

1

=

1

+

4

sin

(

A

2

)

sin

(

B

2

)

sin

(

C

2

)

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