Math, asked by katerajanikumari36, 1 month ago

proof of cot 3A=3cotA-cot cube A/1-3cot square A​

Answers

Answered by sonujmp
0

Answer:

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Answered by affanmuhammed030
2

Step-by-step explanation:

Answer

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cot3A=

sin3A

cos3A

⟶(1)

We know that

cos3A=4cos

3

A−3cosA⟶(2)

sin3A=3sinA−4sin

3

A⟶(3)

Substituting (2) and (3) in (1) we get

cot3A=

3sinA−4sin

3

A

4cos

3

A−3cosA

=

sinA(3−4sin

2

A)

cosA(4cos

2

A−3)

=cotA(

3−4sin

2

A

4cos

2

A−3

)

=cotA(

3(sin

2

A+cos

2

A)−4sin

2

A

4cos

2

A−3×(sin

2

A+cos

2

A)

)(∵sin

2

A+cos

2

A=1)

=cotA(

3cos

2

A+3sin

2

A−4sin

2

A

4cos

2

A−3cos

2

A−3sin

2

A

)

=cotA(

3cos

2

A−sin

2

A

cos

2

A−3sin

2

A

)

=cotA×

sin

2

A

sin

2

A

(

3cos

2

A/sin

2

A−1

cos

2

A/sin

2

A−3

)

=cotA(

3cot

2

A−1

cot

2

A−3

)

=

3cot

2

A−1

cot

3

A−3cotA

=

1−3cot

2

A

3cotA−cot

3

A

Hence proved.

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