Is cos^2(t)=((1+cos(2t)))/2 ?

The answer to whether cos^2(t)=((1+cos(2t)))/2 is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos^2(t)=((1+cos(2t)))/2

prove

cos^{2} (t) = \frac{( 1 + cos ( 2 t ) )}{2}

True

Solution steps

cos^{2} (t) = \frac{1 + cos ( 2 t )}{2}

Manipulating right side

\frac{1 + cos ( 2 t )}{2}

Rewrite using trig identities

\frac{1 + cos ( 2 t )}{2}

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= \frac{1 + 2 cos ^{2} ( t ) - 1}{2}

Simplify

\frac{1 + 2 cos ^{2} ( t ) - 1}{2} : cos^{2} (t)

\frac{1 + 2 cos ^{2} ( t ) - 1}{2}

1 + 2 cos^{2} (t) - 1 = 2 cos^{2} (t)

1 + 2 cos^{2} (t) - 1

Group like terms

= 2 cos^{2} (t) + 1 - 1

1 - 1 = 0

= 2 cos^{2} (t)

= \frac{2 cos ^{2} ( t )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (t)

= cos^{2} (t)

= cos^{2} (t)

We showed that the two sides could take the same form

\Rightarrow True

cos (- \frac{π}{6}) = sin (\frac{2 π}{3})

sin (x + π) - sin (x) + 1 = 0

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

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

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

Is cos^2(t)=((1+cos(2t)))/2 ?
The answer to whether cos^2(t)=((1+cos(2t)))/2 is True