Question

tan61=cos16+sin16/cos16-sin16

Answer 1

Answer:HELLO!

Step-by-step explanation:

Answer 2

Concept

The tan (a + b) equation for  compound angles (a + b) is called the tangent addition equation in trigonometry. The  formula for tan (a + b) can be written as:

 tan (a + b) = (tan a + tan b) / (1-tan a tan  b)

Given

We have given  $tan61=\frac{cos16+sin16}{cos16-sin16}$ .

Find

We are asked to prove given term.

Solution

In the given term LHS $=tan61$ and RHS $=\frac{cos16+sin16}{cos16-sin16}$ .

So we will take LHS $=tan61$

Putting $a=45\textdegree,b=15\textdegree$ in the tan(a+b) formula , we get

$tan61=tan(45+16)\\\\=\frac{tan45+tan16}{1-tan45tan16}$

As we know that $tan45=1$ putting this in above formula , we get

$=\frac{tan45+tan16}{1-tan45tan16}\\\\=\frac{1+tan16}{1-tan16}\\\\=\frac{1+\frac{sin16}{cox16} }{1-\frac{sin16}{cos16} }$

On simplifying, we get

$LHS=\frac{cos16+sin16}{cos16-sin16}$

Therefore LHS = RHS

Hence, it proved that tan61=cos16+sin16/cos16-sin16 .

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