Question

Anyone help me here please!!!!​

Answer 1

here is a formulae

cos2A= 2cos square a -1

Explanation:

as given cos A= 1/2 (a+1/a)

by simplifying

cosA =a²+1/2a

now by following the formulae

cos2A = 2cos²A-1

=2(a²+1/2a)² -1

=2(a⁴+2a²+1/4a²)-1

=a⁴+2a²+1/2a² -1

=a⁴+2a²+1-2a²/2a²

=a⁴+1/2a²

=1/2 (a⁴+1/a²)

=1/2(a⁴/a²+1/a²)

=1/2(a²+1/a²)

{proved}

please mark me as a brainilist...plzzz

thank uuu

Answer 2

Answer: see proof below

Explanation:

Use the Double Angle Identity: cos 2A = 2cos²A - 1

Proof LHS → RHS

Given:
`\cos A=(1)/(2)\bigg(a+(1)/(a)\bigg)`

LHS: cos 2A

Double Angle Identity: 2(cos²A) - 1

`=2\bigg((1)/(2)\bigg(a+(1)/(a)\bigg)^2\bigg)-1`

Simplify:
`2\bigg((1)/(4)\bigg(a^2+2+(1)/(a^2)\bigg)\bigg)-1`

`=(1)/(2)\bigg(a^2+2+(1)/(a^2)\bigg)-1`

`=(1)/(2)a^2+1+(1)/(2a^2)-1`

`=(1)/(2)a^2+(1)/(2a^2)`

Factor:
`=(1)/(2)\bigg(a^2+(1)/(a^2)\bigg)`

`(1)/(2)\bigg(a^2+(1)/(a^2)\bigg)=(1)/(2)\bigg(a^2+(1)/(a^2)\bigg)\quad \checkmark`