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December 20, 2014

December 20, 2014

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

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 5:38pmSince 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.

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