What is the value of sqrt(2)csc(-765)+2csc(742.5) ?

The value of sqrt(2)csc(-765)+2csc(742.5) is -2+2(2sqrt(2-\sqrt{2)}+sqrt(2)sqrt(2-\sqrt{2)})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(2)csc(-765)+2csc(742.5)

2 csc (- 76 5^{\circ}) + 2 csc (742. 5^{\circ})

- 2 + 2 (2 2 - 2 + 2 2 - 2)

Solution steps

2 csc (- 76 5^{\circ}) + 2 csc (742. 5^{\circ})

Use the following property:

csc (- x) = - csc (x)

csc (- 76 5^{\circ}) = - csc (76 5^{\circ})

= 2 (- csc (76 5^{\circ})) + 2 csc (742. 5^{\circ})

csc (76 5^{\circ}) = csc (4 5^{\circ})

= 2 (- csc (4 5^{\circ})) + 2 csc (742. 5^{\circ})

csc (742. 5^{\circ}) = csc (22. 5^{\circ})

= 2 (- csc (4 5^{\circ})) + 2 csc (22. 5^{\circ})

Simplify

= - 2 csc (4 5^{\circ}) + 2 csc (22. 5^{\circ})

Use the following trivial identity:

csc (4 5^{\circ}) = 2

Rewrite using trig identities:

csc (22. 5^{\circ}) = 2 2 - 2 + 2 2 - 2

= - 22 + 2 (2 2 - 2 + 2 2 - 2)

Simplify

- 22 + 2 (2 2 - 2 + 2 2 - 2) : - 2 + 2 (2 2 - 2 + 2 2 - 2)

= - 2 + 2 (2 2 - 2 + 2 2 - 2)

arccos (\frac{13}{6 \cdot 86})

sec (1 0^{\circ})

1 - sin (1)

arcsin (\frac{2}{4})

cos (32 0^{\circ})

What is the value of sqrt(2)csc(-765)+2csc(742.5) ?
The value of sqrt(2)csc(-765)+2csc(742.5) is -2+2(2sqrt(2-\sqrt{2)}+sqrt(2)sqrt(2-\sqrt{2)})