Question

how to prove each equation is not a trigonometric identity by producing a counterexample. sin theta cos theta = cot theta

Answer 1

Just assume one value of theta, say, theta = 30
substitute in both sides of equation.
if left side does not equal right side, then its not an identity.

Answer 2

oh okay thank you. because to substitute both sides i put 2pie/3

Answer 3

and then i got root 3/2 and -1/2 =1

Answer 4

but im not sure what to do next

Answer 5

if you are substituting x=30 degrees, it'll be x=pi/6 radians.
find sin pi/6 and cos pi/6 then.

Answer 6

how come pi/6 radians? is there a reason i can't use like pi/ 4 radians? just curious

Answer 7

you can use any angle.... even pi/4
i just took a particular angle.

Answer 8

oh i see. thank you again.

Answer 9

but first you would start we degrees and then change it to radians right?

Answer 10

*with

Answer 11

if you know the ratios in degrees, then you can use degrees also.
like sin =/ directly.

Answer 12

sin 30 =1/2 *

Answer 13

could you help me with problem too sec ^2 x - 1 = cos x/ csc x

Answer 14

if you put x=pi/4 or 45 degrees, left side not equal to right side.
so, not an identity.