Posted by **Carol** on Monday, January 3, 2011 at 5:30pm.

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.

- trig -
**Reiny**, Monday, January 3, 2011 at 5:38pm
Since all angles are x/2, why not replace them with Ų

so you are asking to prove:

-sinŲ/(2sinŲ+cosŲ) = 1/(4tanŲ + 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 Ų, 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.

## Answer this Question

## Related Questions

- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- algebra - Can someone please help me do this problem? That would be great! ...
- trig - Third time is the charm? I'll try again. Could someone show me how, (- ...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- trig - The expression 4 sin x cos x is equivalent to which of the following? (...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- trigonometry HELP pleasE! - these must be written as a single trig expression, ...