Solve sin(105°) sin(15°)

Question

Calculate the value

\frac{1}{4}

Alternative Form

0.25

Evaluate

sin (10 5^{\circ}) sin (1 5^{\circ})

Calculate the trigonometric value

More Steps

Evaluate

sin (10 5^{\circ})

Rewrite the expression

sin (4 5^{\circ} + 6 0^{\circ})

Use sin (u + v) = sin (u) cos (v) + cos (u) sin (v) to transform the expression

sin (4 5^{\circ}) cos (6 0^{\circ}) + cos (4 5^{\circ}) sin (6 0^{\circ})

Multiply the terms

More Steps

Evaluate

sin (4 5^{\circ}) cos (6 0^{\circ})

Calculate the trigonometric value

\frac{2}{2} cos (6 0^{\circ})

Calculate the trigonometric value

\frac{2}{2} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{2}{2 \times 2}

Multiply the numbers

\frac{2}{4}

\frac{2}{4} + cos (4 5^{\circ}) sin (6 0^{\circ})

Multiply the terms

More Steps

Evaluate

cos (4 5^{\circ}) sin (6 0^{\circ})

Calculate the trigonometric value

\frac{2}{2} sin (6 0^{\circ})

Calculate the trigonometric value

\frac{2}{2} \times \frac{3}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{2 \times 3}{2 \times 2}

Multiply the numbers

\frac{6}{2 \times 2}

Multiply the numbers

\frac{6}{4}

\frac{2}{4} + \frac{6}{4}

Write all numerators above the common denominator

\frac{2 + 6}{4}

\frac{2 + 6}{4} \times sin (1 5^{\circ})

Calculate the trigonometric value

More Steps

Transform the expression

sin (1 5^{\circ})

Use sin (t) = \pm \frac{1 - cos ( 2 t )}{2} to transform the expression

\frac{1 - cos ( 3 0 ^{\circ} )}{2}

Subtract the terms

More Steps

Simplify

1 - cos (3 0^{\circ})

Rewrite the expression

1 - \frac{3}{2}

Reduce fractions to a common denominator

\frac{2}{2} - \frac{3}{2}

Write all numerators above the common denominator

\frac{2 - 3}{2}

\frac{\frac{2 - 3}{2}}{2}

Divide the terms

More Steps

Evaluate

\frac{\frac{2 - 3}{2}}{2}

Multiply by the reciprocal

\frac{2 - 3}{2} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{2 - 3}{2 \times 2}

Multiply the numbers

\frac{2 - 3}{4}

\frac{2 - 3}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{2 - 3}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2 - 3}{2}

\frac{2 + 6}{4} \times \frac{2 - 3}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{( 2 + 6 ) 2 - 3}{4 \times 2}

Multiply the numbers

More Steps

Evaluate

(2 + 6) 2 - 3

Apply the distributive property

2 \times 2 - 3 + 6 \times 2 - 3

Multiply the numbers

More Steps

Evaluate

2 \times 2 - 3

The product of roots with the same index is equal to the root of the product

2 (2 - 3)

Calculate the product

4 - 23

Use a^{2} - 2 ab + b^{2} = (a - b)^{2} to factor the expression

(3 - 1)^{2}

Reduce the index of the radical and exponent with 2

3 - 1

3 - 1 + 6 \times 2 - 3

Multiply the numbers

More Steps

Evaluate

6 \times 2 - 3

The product of roots with the same index is equal to the root of the product

6 (2 - 3)

Calculate the product

12 - 63

Use a^{2} - 2 ab + b^{2} = (a - b)^{2} to factor the expression

(3 - 3)^{2}

Reduce the index of the radical and exponent with 2

3 - 3

3 - 1 + 3 - 3

Since two opposites add up to 0,remove them form the expression

- 1 + 3

Add the numbers

2

\frac{2}{4 \times 2}

Multiply the numbers

\frac{2}{8}

Solution

\frac{1}{4}

Alternative Form

0.25

Show Solution