What is the value of (sin(150)+cos(300))/(tan(225)-sin(300)) ?

The value of (sin(150)+cos(300))/(tan(225)-sin(300)) is 2(2-sqrt(3))

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(sin(150)+cos(300))/(tan(225)-sin(300))

\frac{sin ( 15 0 ^{\circ} ) + cos ( 30 0 ^{\circ} )}{tan ( 22 5 ^{\circ} ) - sin ( 30 0 ^{\circ} )}

2 (2 - 3)

Solution steps

\frac{sin ( 15 0 ^{\circ} ) + cos ( 30 0 ^{\circ} )}{tan ( 22 5 ^{\circ} ) - sin ( 30 0 ^{\circ} )}

tan (22 5^{\circ}) = tan (4 5^{\circ})

= \frac{sin ( 15 0 ^{\circ} ) + cos ( 30 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) - sin ( 30 0 ^{\circ} )}

Rewrite using trig identities:

cos (30 0^{\circ}) = 1 - 2 sin^{2} (15 0^{\circ})

= \frac{sin ( 15 0 ^{\circ} ) + 1 - 2 sin ^{2} ( 15 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) - sin ( 30 0 ^{\circ} )}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

tan (4 5^{\circ}) = 1

Rewrite using trig identities:

sin (30 0^{\circ}) = - \frac{3}{2}

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

Simplify

\frac{\frac{1}{2} + 1 - 2 ( \frac{1}{2} ) ^{2}}{1 - ( - \frac{3}{2} )} : 2 (2 - 3)

= 2 (2 - 3)

26 cos (5 4^{\circ})

2 + sin (\frac{π}{6})

sin (180 0^{\circ})

π sin (π) + cos (π)

sin (15 0^{\circ}) + cos (24 0^{\circ}) - tan (31 5^{\circ})

What is the value of (sin(150)+cos(300))/(tan(225)-sin(300)) ?
The value of (sin(150)+cos(300))/(tan(225)-sin(300)) is 2(2-sqrt(3))