What is (cos(x))/(1-sin^2(x)) ?

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

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simplify (cos(x))/(1-sin^2(x))

simplify

\frac{cos ( x )}{1 - sin ^{2} ( x )}

sec (x)

Solution steps

\frac{cos ( x )}{1 - sin ^{2} ( x )}

Simplify

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

= \frac{cos ( x )}{cos ^{2} ( x )}

Apply exponent rule:

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

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

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

Cancel the common factor:

cos (x)

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

Use the basic trigonometric identity:

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

= sec (x)

x^{3} + 2 x^{2} + 2 x

\frac{a ^{2} + 3 a - ab - 3 b}{a ^{2} - ab + 5 a - 5 b}

42 \cdot 53

lo g_{a} (5) + lo g_{a} (x) - lo g_{a} (2)

x^{2} + b x + \frac{b ^{2}}{4}