Question

cos60+sin60÷cos60-sin60

Answer 1

1 +√3/2whole divide by1-√3/2

Answer 2

Answer:

The value of $\frac{cos60+sin60}{cos60-sin60}$ = -(2+√3)

Step-by-step explanation:

To find,

The value of $\frac{cos60+sin60}{cos60-sin60}$

Solution:

Recall the values

cos60 = $\frac{1}{2}$

sin60 = $\frac{\sqrt{3} }{2}$

$\frac{cos60+sin60}{cos60-sin60}$ = $\frac{\frac{1}{2}+\frac{\sqrt{3}}{2} }{\frac{1}{2}-\frac{\sqrt{3}}{2}} }$

=$\frac{\frac{1+\sqrt{3} }{2} }{\frac{1-\sqrt{3} }{2} }$

= $\frac{1+\sqrt{3} }{1-\sqrt{3} }$

Now we need to rationalize the denominator

The rationalizing factor is 1+√3

Multiplying and dividing with the rationalizing factor we get,

$\frac{1+\sqrt{3} }{1-\sqrt{3} }$× $\frac{1+\sqrt{3} }{1+\sqrt{3} }$  $= \frac{(1+\sqrt{3})^2}{1^2-(\sqrt{3})^2 }$

= $\frac{1+3+2\sqrt{3} }{1-3}$

= $\frac{4+2\sqrt{3} }{-2}$

= -(2+√3)

∴ The value of $\frac{cos60+sin60}{cos60-sin60}$ = -(2+√3)

#SPJ3