What is the value of 2sin(52.5)sin(97.5) ?

The value of 2sin(52.5)sin(97.5) is (sqrt(2)+sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(52.5)sin(97.5)

2 sin (52. 5^{\circ}) sin (97. 5^{\circ})

\frac{2 + 3}{2}

Solution steps

2 sin (52. 5^{\circ}) sin (97. 5^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ}) - cos (15 0^{\circ})

= cos (4 5^{\circ}) - cos (15 0^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

= \frac{2}{2} - (- \frac{3}{2})

Simplify

\frac{2}{2} - (- \frac{3}{2}) : \frac{2 + 3}{2}

= \frac{2 + 3}{2}

sin (2 arccos (\frac{4}{5}))

sin (arccos (\frac{8}{17}))

tan (\frac{- π}{12})

sin (\frac{4 π}{4})

2 sin^{2} (π)

What is the value of 2sin(52.5)sin(97.5) ?
The value of 2sin(52.5)sin(97.5) is (sqrt(2)+sqrt(3))/2