Question

Find the value (sin30+cos30)-(sin60+cos30)

Answer 1

Step-by-step explanation:

We Have :-

(sin30+cos30)-(sin60+cos30)

To Find :-

Its value

Solution :-

$we \: know \: that \\ \\ \\ \sin(30) = \dfrac{1}{2} \\ \\ \\ \sin(60) = \dfrac{ \sqrt{3} }{2} \\ \\ \\ \cos(30) = \dfrac{ \sqrt{3} }{2} \\ \\ \\ ( \sin(30) + \cos(30) ) - ( \sin(60) + \cos(30) ) \\ \\ \\ putting \: values \\ \\ \\ (\dfrac{1}{2} + \dfrac{ \sqrt{3} }{2}) - (\dfrac{ \sqrt{3} }{2} + \dfrac{ \sqrt{3} }{2}) \\ \\ \\ ( \dfrac{1 + \sqrt{3} }{2} ) - ( \dfrac{2 \sqrt{3} }{2} ) \\ \\ \\ \dfrac{1 + \sqrt{3} - 2 \sqrt{3} }{2} \\ \\ \\ \dfrac{1 - \sqrt{3}}{2}$

Answer 2

★Given:-

→Sin30°=$\frac{1}{2}$

→Cos30°=$\frac{\sqrt{3}}{2}$

→Sin60°=$\frac{\sqrt{3}}{2}$

$\rule{200}{1}$

★To find:-

The Value of (Sin30+Cos30)-(Sin60+Cos30)

$\rule{200}{1}$

★Proof:-

★Refer Given for the Values★

→($\frac{1}{2}$-$\frac{\sqrt{3}}{2}$)-($\frac{\sqrt{3}}{2}$-$\frac{\sqrt{3}}{2}$)

→($\frac{1+ \sqrt{3}}{2}$)-($\frac{2\sqrt{3}}{2}$)

→$\frac{1-\sqrt{3}}{2}$

$\rule{200}{1}$