Math, asked by tannusharma2061, 1 month ago

Prove the following identities: ​

Attachments:

Answers

Answered by thehappyqueen
0

cos3A=4cos

3

A−3cosA

and

sin3A=3sinA−4sin

3

A

Using these in LHS,

∴ The L.H.S =cos

3

A(4cos

3

A−3cosA)+sin

3

A(3sinA−4sin

3

A)

⇒4cos

6

A−3cos

4

A+3sin

4

A−4sin

6

A

⇒4(cos

6

A−sin

6

A)−3(cos

4

A−sin

4

A)

⇒4{(cos

2

A)

3

−(sin

2

A)

3

}−3{(cos

2

A)

2

−(sin

2

A)

2

}

⇒4{cos

2

A−sin

2

A}{(cos

2

A)

2

+cos

2

Asin

2

A+(sin

2

A)

2

}−3(cos

2

A−sin

2

A)(cos

2

A+sin

2

A)

⇒(cos

2

A−sin

2

A)[4{(cos

2

A)

2

+cos

2

Asin

2

A+(sin

2

A)

2

}−3.1]

⇒(cos

2

A−sin

2

A)[4cos

2

A+4cos

2

Asin

2

A+4sin

4

A−3(cos

2

A+sin

2

A)

2

]

⇒(cos

2

A−sin

2

A)[4cos

4

A+4cos

2

Asin

2

A+4sin

4

A−3(cos

4

A+2cos

2

Asin

2

A+sin

4

A)]

⇒(cos

2

A−sin

2

A)[cos

4

A−2cos

2

Asin

2

A+sin

4

A]

⇒(cos

2

A−sin

2

A)(cos

2

A−sin

2

A)

2

,

⇒(cos

2

A−sin

2

A)

3

⇒(cos2A)

3

⇒cos

3

2A

=RHS Hence proved

Similar questions