What is 1/(sec^2(x))dx ?

The solution to 1/(sec^2(x))dx is cos^2(x)dx

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simplify 1/(sec^2(x))dx

simplify

\frac{1}{sec ^{2} ( x )} d x

cos^{2} (x) d x

Solution steps

\frac{1}{sec ^{2} ( x )} d x

Multiply fractions:

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

= \frac{1 \cdot d x}{sec ^{2} ( x )}

Multiply:

1 \cdot d x = d x

= \frac{d x}{sec ^{2} ( x )}

Use the basic trigonometric identity:

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

= d x cos^{2} (x)

1 - (sin (t))^{2}

(\frac{1 + cos ( 2 θ )}{2}) d θ

cos^{2} (\frac{π}{2} + x)

3 cos (- \frac{5}{6} π + x)

2 sin (x + \frac{π}{6})