Question

Which of the following are identities? Check all that apply

Answer 1

A, B, and C are all correct. APEX

Explanation:

Answer 2

A, C

Explanation:

Actually, those questions require us to develop those equations to derive into trigonometrical equations so that we can unveil them or not. Doing it only two alternatives, the other ones will not result in Trigonometrical Identities.

Examining

A) True

`(1-tan^(2)x)/(2tanx) =(1)/(tan2x) \\ (1-tan^(2)x)/(2tanx) =(1)/((2tanx)/(1-tan^(2)x))\\ tan2x=(1-tan^(2)x)/(2tanx)`

Double angle
`tan2\alpha =(1 -tan^(2)\alpha )/(2tan\alpha)`

B) False,

No further development towards a Trig Identity

C) True

Double Angle Sine Formula
`sin2\alpha =2sin\alpha *cos\alpha`

`sin(8x)=2sin(4x)cos(4x)\\2sin(4x)cos(4x)=2sin(4x)cos(4x)`

D) False No further development towards a Trig Identity

`[sin(x)-cos(x)]^(2) =1+sin(2x)\\ sin^(2) (x)-2sin(x)cos(x)+cos^(2)x=1+2sinxcosx\\ \\sin^(2) (x)+cos^(2)x=1+4sin(x)cos(x)`