What is the value of sin(75)cos(15)+sin(15)cos(75) ?

The value of sin(75)cos(15)+sin(15)cos(75) is 1

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sin(75)cos(15)+sin(15)cos(75)

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

1

Solution steps

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

Rewrite as

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

Rewrite using trig identities:

sin (9 0^{\circ})

= sin (9 0^{\circ})

Use the following trivial identity:

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

= 1

arcsec (\frac{π}{2})

\frac{2 tan ( \frac{7 π}{8} )}{1 - 2 tan ^{2} ( \frac{7 π}{8} )}

arccos (\frac{2}{7})

arccos (\frac{5}{5 10})

10 \cdot tan (2 5^{\circ})

What is the value of sin(75)cos(15)+sin(15)cos(75) ?
The value of sin(75)cos(15)+sin(15)cos(75) is 1