What is the value of sin(165)cos(75) ?

The value of sin(165)cos(75) is (2-sqrt(3))/4

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sin(165)cos(75)

sin (16 5^{\circ}) cos (7 5^{\circ})

\frac{2 - 3}{4}

Solution steps

sin (16 5^{\circ}) cos (7 5^{\circ})

Rewrite using trig identities:

sin (16 5^{\circ}) = sin (1 5^{\circ})

= sin (1 5^{\circ}) cos (7 5^{\circ})

Rewrite using trig identities:

\frac{sin ( 9 0 ^{\circ} ) - sin ( 6 0 ^{\circ} )}{2}

= \frac{sin ( 9 0 ^{\circ} ) - sin ( 6 0 ^{\circ} )}{2}

Use the following trivial identity:

sin (9 0^{\circ}) = 1

Use the following trivial identity:

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

= \frac{1 - \frac{3}{2}}{2}

Simplify

\frac{1 - \frac{3}{2}}{2} : \frac{2 - 3}{4}

= \frac{2 - 3}{4}

2 + sin (\frac{3 π}{4})

arcsin (sec (π))

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

\frac{tan ( 7 1 ^{\circ} ) - tan ( 1 1 ^{\circ} )}{1 + tan ( 7 1 ^{\circ} ) tan ( 1 1 ^{\circ} )}

sin_{- 1} (1)

What is the value of sin(165)cos(75) ?
The value of sin(165)cos(75) is (2-sqrt(3))/4