Question

[cos(x)cos(y)][tan(x)+tan(y)]=sin(x+y)​

Answer 1

Answer:

this is a required answer.

Answer 2

The given identity is proved.

What is trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation

According to the given question we have a trigonometry identity.

$cos(x)cos(y)[tan(x)+tan(y)] = sin(x+y)$

To prove the above the identity, we show that R.H.S = L.H.S

So,

$L.H.S = [cos(x)cos(y)][tan(x)+tany(y)]$

$\implies L.H.S = [cos(x)cos(y)][\frac{sinx}{cosx} +\frac{siny}{cosy} ]$

$\implies L.H.S = [cos(x)cos(y)][\frac{sinxcosy+sinycosx}{cosxcosy} ]$

$\implies L.H.S = cos(x)cos(y) \frac{sin(x)cos(y)+sin(y)cos(x)}{cos(x)cos(y)}$

$\implies L.H.S = sin(x)cos(y)+ sin(y)cos(x)$

$\implies L.H.S = sin(x+y)...(i)$

And from the given trigonometry identity,

$R.H.S = sin(x+y)..(ii)$

Therefore,

L.H.S = R.H.S

⇒ $cos(x)cos(y)[tan(x)+tan(y)] = sin(x+y)$      (proved)

Hence, the given identity is proved.

Find out more information about trigonometric identities here:

https://brainly.com/question/12537661

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