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

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

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

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

1

Solution steps

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

sin (arctan (- 5))

tan (\frac{2}{2})

arccos (- 2)

cos (arcsin (\frac{4}{5}) + arctan (\frac{12}{5}))

2 sec^{2} (\frac{π}{3})

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