What is the value of 40*(sin(135))/(sin(105)) ?

The value of 40*(sin(135))/(sin(105)) is 40(sqrt(3)-1)

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40*(sin(135))/(sin(105))

40 \cdot \frac{sin ( 13 5 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

40 (3 - 1)

Solution steps

40 \cdot \frac{sin ( 13 5 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

Use the following trivial identity:

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

Rewrite using trig identities:

sin (10 5^{\circ}) = \frac{2 ( 3 + 1 )}{4}

= 40 \cdot \frac{\frac{2}{2}}{\frac{2 ( 3 + 1 )}{4}}

Simplify

40 \cdot \frac{\frac{2}{2}}{\frac{2 ( 3 + 1 )}{4}} : 40 (3 - 1)

= 40 (3 - 1)

8 sin (29 0^{\circ}) + 6 sin (6 0^{\circ})

arccos (cos (\frac{π}{12}))

\frac{10}{sin ( 3 6 ^{\circ} )}

4 (sin (15 0^{\circ})) (cos (21 0^{\circ})) + 3 (tan (24 0^{\circ}))

30 sin (1 0^{\circ})

What is the value of 40*(sin(135))/(sin(105)) ?
The value of 40*(sin(135))/(sin(105)) is 40(sqrt(3)-1)