Is sec(x)cos(x)+tan^2(x)=sec^2(x) ?

The answer to whether sec(x)cos(x)+tan^2(x)=sec^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 sec(x)cos(x)+tan^2(x)=sec^2(x)

prove

sec (x) cos (x) + tan^{2} (x) = sec^{2} (x)

True

Solution steps

sec (x) cos (x) + tan^{2} (x) = sec^{2} (x)

Manipulating left side

sec (x) cos (x) + tan^{2} (x)

Rewrite using trig identities

sec (x) cos (x) + tan^{2} (x)

sec (x) cos (x) = 1

sec (x) cos (x)

Express with sin, cos

sec (x) cos (x)

Use the basic trigonometric identity:

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

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

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

\frac{1}{cos ( x )} cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

cos (x)

= 1

= 1

= 1 + tan^{2} (x)

Use the Pythagorean identity:

tan^{2} (x) + 1 = sec^{2} (x)

= sec^{2} (x)

= sec^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ^{2} ( θ ) + 1}{sec ( θ )} = sec (θ)

cot^{2} (θ) + 1 = \frac{1}{sin ^{2} ( θ )}

3 cos (2 x + \frac{π}{2}) - 2 = 6 cos^{2} (x + \frac{π}{4})

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

cot^{4} (x) = \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

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