What is the value of sin(-315)sin(-15) ?

The value of sin(-315)sin(-15) is -(sqrt(3)-1)/4

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sin(-315)sin(-15)

sin (- 31 5^{\circ}) sin (- 1 5^{\circ})

- \frac{3 - 1}{4}

Solution steps

sin (- 31 5^{\circ}) sin (- 1 5^{\circ})

Use the following property:

sin (- x) = - sin (x)

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

= sin (- 31 5^{\circ}) (- sin (1 5^{\circ}))

Use the following property:

sin (- x) = - sin (x)

sin (- 31 5^{\circ}) = - sin (31 5^{\circ})

= (- sin (31 5^{\circ})) (- sin (1 5^{\circ}))

Simplify

= sin (31 5^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

sin (31 5^{\circ}) = - \frac{2}{2}

Rewrite using trig identities:

sin (1 5^{\circ}) = \frac{6 - 2}{4}

= (- \frac{2}{2}) \frac{6 - 2}{4}

Simplify

(- \frac{2}{2}) \frac{6 - 2}{4} : - \frac{3 - 1}{4}

= - \frac{3 - 1}{4}

csc (- \frac{13 π}{6})

tan (12. 5^{\circ})

\frac{1}{2} arctan (3)

cos^{2} (\frac{π}{4}) - sin (\frac{7 π}{6})

cot^{2} (6 0^{\circ})

What is the value of sin(-315)sin(-15) ?
The value of sin(-315)sin(-15) is -(sqrt(3)-1)/4