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

The value of sin(52.5)cos(7.5) is (sqrt(3)+sqrt(2))/4

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sin(52.5)cos(7.5)

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

\frac{3 + 2}{4}

Solution steps

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

Rewrite using trig identities:

\frac{sin ( 6 0 ^{\circ} ) + sin ( 4 5 ^{\circ} )}{2}

= \frac{sin ( 6 0 ^{\circ} ) + sin ( 4 5 ^{\circ} )}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

= \frac{\frac{3}{2} + \frac{2}{2}}{2}

Simplify

\frac{\frac{3}{2} + \frac{2}{2}}{2} : \frac{3 + 2}{4}

= \frac{3 + 2}{4}

cos (1 5^{\circ}) cos (4 5^{\circ}) - sin (1 5^{\circ}) sin (4 5^{\circ})

cos (1.8)

tan^{2} (+ 1)

csc (arctan (- \frac{5}{12}))

- 3 sin (\frac{3 π}{2})

What is the value of sin(52.5)cos(7.5) ?
The value of sin(52.5)cos(7.5) is (sqrt(3)+sqrt(2))/4