Question

sin 60 +cos 60 / sin60- cos 60. plis solve​

Answer 1

Answer:

1/2+√3/2÷1/2-√3/2 =1+√3/2×2/√3-1 =-(√3+1)/(√3-1)

Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{ \sin {60}^{ \circ} + \cos {60}^{ \circ}}{\sin {60}^{ \circ} - \cos {60}^{ \circ}} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ \frac{ \sin {60}^{ \circ} + \cos {60}^{ \circ}}{\sin {60}^{ \circ} - \cos {60}^{ \circ}} }$

We simplify it as below

$\displaystyle \sf{ \frac{ \sin {60}^{ \circ} + \cos {60}^{ \circ}}{\sin {60}^{ \circ} - \cos {60}^{ \circ}} }$

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

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

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

$\displaystyle \sf{ = \frac{ (\sqrt{3} + 1)(\sqrt{3} + 1)}{ (\sqrt{3} + 1)(\sqrt{3} - 1) } }$

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

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

$\displaystyle \sf{ = \frac{ 4+ 2 \sqrt{3} }{ 2} }$

$\displaystyle \sf{ = \frac{ 2(2+ \sqrt{3} )}{ 2} }$

$\displaystyle \sf{ = 2+ \sqrt{3} }$

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