Is 1+cos^2(x)=2cos^2(x)+sin^2(x) ?

The answer to whether 1+cos^2(x)=2cos^2(x)+sin^2(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove 1+cos^2(x)=2cos^2(x)+sin^2(x)

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

2 cos^{2} (x) + 1 - cos^{2} (x) : cos^{2} (x) + 1

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

Group like terms

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

Add similar elements:

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

= cos^{2} (x) + 1

= cos^{2} (x) + 1

= cos^{2} (x) + 1

= 1 + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (x) = 2

sin (x) csc^{2} (x) = \frac{1}{sin ( x )}

\frac{cos ( 2 θ )}{cos ^{2} ( θ )} = 1 - tan^{2} (θ)

(tan (θ + 1)) = sec (θ)

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