Question

Which of the following are trigonometric identities? check all that apply.(Need help asap)

Answer 1

A. Yes:


`(\sin(x+y))/(\sin x\cos y)=(\sin x\cos y+\cos x\sin y)/(\sin x\cos y)=1+\cot x\tan y`

B. Yes:


`(\csc x-\sin x)/(\csc x)=1-\frac{\sin x}{\frac1{\sin x}}=1-\sin^2x=\cos^2x`

C. Yes:


`\tan x\cos x\csc x=(\sin x)/(\cos x)\cdot\cos x\cdot\frac1{\sin x}=1`

D. No: if
`x=0`, then
`4\cos0\sin0=0`, but
`2\cos0+1-2\sin0=3`.

Answer 2

(A), (B) and (C)

Explanation:

(A) The given statement is:

`(sin(x+y))/(sinxcosy)=1+cotxtany`

Upon solving, we have

`(sin(x+y))/(sinxcosy)=(sinxcosy+cosxsiny)/(sinxcosy)=1+cotxtany`

Thus, it is a trigonometric identity.

(B) The given statement is:

`(cscx-sinx)/(cscx)=cos^2x`

Upon solving, we have

`(cscx-sinx)/(cscx)=1-(sinx)/((1)/(sinx))}=1-sin^2x=cos^2x`

Thus, it is a trigonometric identity.

(C) The given statement is:

`tanxcosxcscx=1`

Upon solving, we have

`tanxcosxcscx=(sinx)/(cosx){\cdot}cosx{\cdot}(1)/(sinx)=1`

Thus, it is a trigonometric identity.

(D) The given statement is:

`4cosxsinx=2cosx+1-2sinx`

Now, if x=0, then

`4cos0sin0=0` but
`2cos0+1-2sin0=3`

Thus, it is not a trigonometric identity.