What is expand ((cos(x)+sin(x))^2)/(cos^2(x)) ?

The solution to expand ((cos(x)+sin(x))^2)/(cos^2(x)) is 1/(cos^2(x))+(sin(2x))/(cos^2(x))

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expand ((cos(x)+sin(x))^2)/(cos^2(x))

expand

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

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

Solution steps

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

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

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

Rewrite using trig identities

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

Apply the fraction rule:

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

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

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

\frac{9 - r ^{3} - r ^{2}}{( 3 r ^{2} - 5 r + 2 ) ^{2}}

(e^{3 t} + 3 e^{3 t} t)^{2}

\frac{10}{s ( s + 5 )}

(y + 6) (y + 2)^{2} d y

5760 \cdot (- 625 s + 188 π^{2} \cdot (3 s + 1280))

What is expand ((cos(x)+sin(x))^2)/(cos^2(x)) ?
The solution to expand ((cos(x)+sin(x))^2)/(cos^2(x)) is 1/(cos^2(x))+(sin(2x))/(cos^2(x))