What is the value of tan(70)+cot(20)-2tan(70) ?

The value of tan(70)+cot(20)-2tan(70) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(70)+cot(20)-2tan(70)

tan (7 0^{\circ}) + cot (2 0^{\circ}) - 2 tan (7 0^{\circ})

0

Solution steps

tan (7 0^{\circ}) + cot (2 0^{\circ}) - 2 tan (7 0^{\circ})

Simplify

= - tan (7 0^{\circ}) + cot (2 0^{\circ})

Rewrite using trig identities:

tan (7 0^{\circ}) = cot (2 0^{\circ})

tan (7 0^{\circ})

Use the following identity:

tan (x) = cot (9 0^{\circ} - x)

cot (9 0^{\circ} - x)

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{cos ( 9 0 ^{\circ} - x )}{sin ( 9 0 ^{\circ} - x )}

Use the Angle Difference identity:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= \frac{cos ( 9 0 ^{\circ} ) cos ( x ) + sin ( 9 0 ^{\circ} ) sin ( x )}{sin ( 9 0 ^{\circ} - x )}

Use the Angle Difference identity:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= \frac{cos ( 9 0 ^{\circ} ) cos ( x ) + sin ( 9 0 ^{\circ} ) sin ( x )}{sin ( 9 0 ^{\circ} ) cos ( x ) - cos ( 9 0 ^{\circ} ) sin ( x )}

Use the following trivial identity:

cos (9 0^{\circ}) = 0

Use the following trivial identity:

sin (9 0^{\circ}) = 1

= \frac{0 cos ( x ) + 1 sin ( x )}{1 cos ( x ) - 0 sin ( x )}

Simplify

= \frac{sin ( x )}{cos ( x )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

= cot (9 0^{\circ} - 7 0^{\circ})

Simplify

= cot (2 0^{\circ})

= - cot (2 0^{\circ}) + cot (2 0^{\circ})

Simplify

= 0

50 cos (3 8^{\circ})

arctan ((tan (1^{\circ}))^{2} + (tan (4^{\circ}))^{2})

cos^{2} (\frac{5 π}{4}) - sin^{2} (\frac{2 π}{3})

50 sin (5 3^{\circ})

arcsin (2 sin (3 0^{\circ}))

What is the value of tan(70)+cot(20)-2tan(70) ?
The value of tan(70)+cot(20)-2tan(70) is 0