Question

find the value of cos 30°+ sin 60° ÷ 1+ cos 60° + sin 30 °

Answer 1

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Answer 2

Given,

$\frac{ \cos30 \degree \: + \sin60 \degree \: }{1 + \cos60 \degree + sin30 \degree }$

As we know that,

$\cos30 \degree \: = \frac{ \sqrt{3} }{2}$

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

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

$\sin30 \degree \: = \frac{1}{2}$

Now, substitute the values.

$\frac{ \cos30 \degree \: + \sin60 \degree \: }{1 + \cos60 \degree + sin30 \degree }$

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

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

$\frac{ \frac{2 \sqrt{3} }{2} }{ \frac{4}{2} }$

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

$\frac{2 \sqrt{3} }{2} \times \frac{1}{2}$

$\frac{2 \sqrt{3} }{4}$

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

Therefore the value is √3/2.

Additional information:

●Sin A = 1/ Cosec A

● Cos A = 1/Sec A

● Tan A = 1/Cot A

● Tan A = Sin A/Cos A

● Cot A = Cos A/Sin A