Is cos(2a)=cos^2(a)-sin^2(a) ?

The answer to whether cos(2a)=cos^2(a)-sin^2(a) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(2a)=cos^2(a)-sin^2(a)

prove

cos (2 a) = cos^{2} (a) - sin^{2} (a)

True

Solution steps

cos (2 a) = cos^{2} (a) - sin^{2} (a)

Manipulating left side

cos (2 a)

Rewrite using trig identities

cos (2 a)

Rewrite as

= cos (a + a)

Use the Angle Sum identity:

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

= cos (a) cos (a) - sin (a) sin (a)

= cos (a) cos (a) - sin (a) sin (a)

Simplify

cos (a) cos (a) - sin (a) sin (a) : cos^{2} (a) - sin^{2} (a)

cos (a) cos (a) - sin (a) sin (a)

cos (a) cos (a) = cos^{2} (a)

cos (a) cos (a)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

cos (a) cos (a) = cos^{1 + 1} (a)

= cos^{1 + 1} (a)

Add the numbers:

1 + 1 = 2

= cos^{2} (a)

sin (a) sin (a) = sin^{2} (a)

sin (a) sin (a)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (a) sin (a) = sin^{1 + 1} (a)

= sin^{1 + 1} (a)

Add the numbers:

1 + 1 = 2

= sin^{2} (a)

= cos^{2} (a) - sin^{2} (a)

= cos^{2} (a) - sin^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) + cot (θ) = sec (θ) \cdot csc (θ)

\frac{cos ( x )}{csc ( x ) + 1} + \frac{cos ( x )}{csc ( x ) - 1} = 2 tan (x)

\frac{cos ( x ) csc ( x )}{cot ^{2} ( x )} = tan (x)

sin^{2} (θ) - cos^{2} (θ) = 2 sin^{2} (θ) - 1

cot (\frac{π}{2} - u) = tan (u)

Is cos(2a)=cos^2(a)-sin^2(a) ?
The answer to whether cos(2a)=cos^2(a)-sin^2(a) is True