What is the value of sin^2(35)+sin^2(55) ?

The value of sin^2(35)+sin^2(55) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(35)+sin^2(55)

sin^{2} (3 5^{\circ}) + sin^{2} (5 5^{\circ})

1

Solution steps

sin^{2} (3 5^{\circ}) + sin^{2} (5 5^{\circ})

Rewrite using trig identities:

sin (5 5^{\circ}) = cos (3 5^{\circ})

sin (5 5^{\circ})

Use the following identity:

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

= cos (9 0^{\circ} - 5 5^{\circ})

Simplify

= cos (3 5^{\circ})

= sin^{2} (3 5^{\circ}) + cos^{2} (3 5^{\circ})

Rewrite using trig identities:

1

cos^{2} (3 5^{\circ}) + sin^{2} (3 5^{\circ})

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= 1

= 1

sin (\frac{18 π}{3})

cos^{2} (1) - e^{- 2 (1)}

π cos (3 π)

7 cos (4 0^{\circ})

- 4 sin (\frac{5 π}{6})

What is the value of sin^2(35)+sin^2(55) ?
The value of sin^2(35)+sin^2(55) is 1