What is the value of sin(75)-sin(15) ?

The value of sin(75)-sin(15) is (sqrt(2))/2

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sin(75)-sin(15)

sin (7 5^{\circ}) - sin (1 5^{\circ})

\frac{2}{2}

Solution steps

sin (7 5^{\circ}) - sin (1 5^{\circ})

Rewrite using trig identities:

2 sin (3 0^{\circ}) cos (4 5^{\circ})

= 2 sin (3 0^{\circ}) cos (4 5^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= 2 \cdot \frac{1}{2} \cdot \frac{2}{2}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{2}{2} : \frac{2}{2}

= \frac{2}{2}

sin (5 1^{\circ})

csc (- \frac{5 π}{4})

sin (arccos (\frac{4}{5}))

cos (\frac{23 π}{12})

sin (20 0^{\circ})

What is the value of sin(75)-sin(15) ?
The value of sin(75)-sin(15) is (sqrt(2))/2