Question

which of the following are trigonometric indentities (check all that apply).
a. 4cos(x)sin(x) = 2cos(x)+1-2sin(x)
b. tan(x)cos(x)csc(x) = 1
c. (csc(x) - sin(x))/csc(x) = cos^2(x)
d. 1 + cot(x) tan(y) = (sin(x+y))/sin(x)cos(y)
Please help! I am really bad with identities!

Answer 1

b is an identity
just check if the left had side equal to right hand side
there is more than one

Answer 2

c as well is an identity

Answer 3

but how would you figure it out

Answer 4

because i would like to know how to prove and show an equation is an identity @xapproachesinfinity

Answer 5

use the identities you know
like csc=1/sin
tan=sin/cos
...
you need to know the basic stuff

Answer 6

a is not good
it is not an identity
4cosxsinx=2sin2x this cannot equal that left side stuff

Answer 7

of course you need to know that 2cosxsinx=sin2x

Answer 8

well now you have only one to work on
recall
sin(a+b)=sinacosb+sinbcosa

Answer 9

yes

Answer 10

use that x=a y=b
see if that satisfies the left hand side

Answer 11

it doesn't

Answer 12

i agree

Answer 13

i think you are done:)

Answer 14

so then the answers are b and c ?

Answer 15

@xapproachesinfinity

Answer 16

yes are you not paying attention hehe

Answer 17

d is also an answer @xapproachesinfinity

Answer 18

No

Answer 19

one trick to check that is to put arbitrary values for x
example

\(\large\tt \begin{align} \color{black}{x=45^{\circ}\hspace{.33em}\\~\\}\end{align}\)

and see if \(\bf LHS =RHS\)

Answer 20

i like this one :) never used in identities