What is the value of sin(135+30) ?

The value of sin(135+30) is (sqrt(6)-sqrt(2))/4

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sin(135+30)

sin (13 5^{\circ} + 3 0^{\circ})

\frac{6 - 2}{4}

Solution steps

sin (13 5^{\circ} + 3 0^{\circ})

Rewrite using trig identities:

sin (13 5^{\circ}) cos (3 0^{\circ}) + cos (13 5^{\circ}) sin (3 0^{\circ})

= sin (13 5^{\circ}) cos (3 0^{\circ}) + cos (13 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

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

Simplify

\frac{2}{2} \cdot \frac{3}{2} + (- \frac{2}{2}) \frac{1}{2} : \frac{6 - 2}{4}

= \frac{6 - 2}{4}

cot (- \frac{6 π}{5})

sin (\frac{π}{6}) cos (\frac{π}{2}) + cos (\frac{π}{6}) sin (\frac{π}{2})

sin (30.9 6^{\circ})

arcsin (\frac{( 2 )}{2})

\frac{sin ( 6 0 ^{\circ} )}{sin ( 3 0 ^{\circ} )}

What is the value of sin(135+30) ?
The value of sin(135+30) is (sqrt(6)-sqrt(2))/4