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

Use the Angle Sum identity:

sin (s) cos (t) + cos (s) sin (t) = sin (s + t)

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

Simplify

= sin (9 0^{\circ})

= sin (9 0^{\circ})

Use the following trivial identity:

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

sin (9 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 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