What is the value of sin(175)cos(125)+cos(175)sin(125) ?

The value of sin(175)cos(125)+cos(175)sin(125) is -(sqrt(3))/2

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sin(175)cos(125)+cos(175)sin(125)

sin (17 5^{\circ}) cos (12 5^{\circ}) + cos (17 5^{\circ}) sin (12 5^{\circ})

- \frac{3}{2}

Solution steps

sin (17 5^{\circ}) cos (12 5^{\circ}) + cos (17 5^{\circ}) sin (12 5^{\circ})

Rewrite using trig identities:

sin (30 0^{\circ})

= sin (30 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

= 0 \cdot (- \frac{1}{2}) + (- 1) \frac{3}{2}

Simplify

= - \frac{3}{2}

sin (6 0^{\circ}) sin (3 0^{\circ})

arctan (\frac{100}{150})

\frac{sin ^{2} ( 2 π )}{2}

arctan (\frac{- 5 3}{- 5})

csc (3 0^{\circ}) + cot (4 5^{\circ}) + sec (6 0^{\circ})

What is the value of sin(175)cos(125)+cos(175)sin(125) ?
The value of sin(175)cos(125)+cos(175)sin(125) is -(sqrt(3))/2