What is the value of sin(52.5)sin(7.5) ?

The value of sin(52.5)sin(7.5) is (sqrt(2)-1)/4

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sin(52.5)sin(7.5)

sin (52. 5^{\circ}) sin (7. 5^{\circ})

\frac{2 - 1}{4}

Solution steps

sin (52. 5^{\circ}) sin (7. 5^{\circ})

Rewrite using trig identities:

\frac{cos ( 4 5 ^{\circ} ) - cos ( 6 0 ^{\circ} )}{2}

= \frac{cos ( 4 5 ^{\circ} ) - cos ( 6 0 ^{\circ} )}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

= \frac{\frac{2}{2} - \frac{1}{2}}{2}

Simplify

\frac{\frac{2}{2} - \frac{1}{2}}{2} : \frac{2 - 1}{4}

= \frac{2 - 1}{4}

sin (arctan (- \frac{4}{3}))

2 cos (\frac{3 π}{4})

cos^{2} (1 8^{\circ})

3 tan (3 0^{\circ})

arcsin (sin (- \frac{5 π}{3}))

What is the value of sin(52.5)sin(7.5) ?
The value of sin(52.5)sin(7.5) is (sqrt(2)-1)/4