Question

I asked below but I guess it was not understood what I was asking. I'll try again.

Could someone show me how,

(- sin (x/2) /( 2 sin (x/2) + cos (x/2))

is an alternate representation for,

1 / ( 4 tan (x/2) + 2 )
TIA
Carol
I know the half-angle formulas are used but I cannot arrive at the above, first, representation.

Answer 1

Since all angles are x/2, why not replace them with Ø

so you are asking to prove:

-sinØ/(2sinØ+cosØ) = 1/(4tanØ + 2)

I noticed that bobpursley checked it using 2 different angles, and the equation was false

To be an identity, it must be true for all values of the angle,
thus the equation is not true, and cannot be proven.

By mere observation, for acute angles of Ø, all trig ratios would be positive.
So we have operations using only positive numbers, so any products, sums or quotient answers would be positive.
But your Left Side is negative, and the Right Side is positive.
Therefore NO CAN DO !

check your question or your typing.