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

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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

p ro v e cot^{2} (θ) + 1 = \frac{1}{sin ^{2} ( θ )}

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

p ro v e cos^{4} (b) - sin^{4} (b) = cos (2 b)

p ro v e sin^{2} (x) sec^{2} (x) = sec^{2} (x) - 1

p ro v e (6 cos^{2} (x) - 6 sin^{2} (x)) = 6 - 12 sin^{2} (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