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Prove the following:$$\frac{\sin x-\sin y}{\cos x+\cos y}=\tan \frac{x-y}{2}$$
01:02
Subhadeepta S.
Precalculus
Chapter 3
Trigonometric Functions
Section 3
Trigonometry
Campbell University
Piedmont College
Harvey Mudd College
Utica College
Lectures
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in this kitchen we have to prove that Synnex negative same way upon core sex while they do goes way equal to then Xnegative Y up on two. So here first of all we take Alleges and we simplify this. So here Alex is equal to sane eggs negative saying why upon Of course eggs ball to do because why? So now here we have a formula for sign E. Bliss, sorry, negative sign be equal to two times. Of course april is B upon to games saying E negative B up on two and goes A plus goes B equal to two times. Of course april is B upon to times of course E now you do be upon to now we apply that formula in allergies. So here allergy is equal to two times of course X positive. Why upon to times sane Xnegative white upon to upon two times of course X plus way upon to games goes xnegative Y upon to. So now we simplify this and here we get saying X plus Y, sorry, acts negative Y upon to Upon goes Xnegative Y up on two equal to then Xnegative Y upon to. So here you can see that that is the value of arches. So here Alex is equal to arches has proved, so it is our final answer.
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