What is expand (cot(x)+tan(x))^2 ?

The solution to expand (cot(x)+tan(x))^2 is csc^2(x)sec^2(x)

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expand (cot(x)+tan(x))^2

expand

(cot (x) + tan (x))^{2}

csc^{2} (x) sec^{2} (x)

Solution steps

(cot (x) + tan (x))^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(cot (x) + tan (x))^{2} = cot^{2} (x) + 2 cot (x) tan (x) + tan^{2} (x)

= cot^{2} (x) + 2 cot (x) tan (x) + tan^{2} (x)

Express with sin, cos

= \frac{cos ^{4} ( x ) + sin ^{4} ( x ) + 2 cos ^{2} ( x ) sin ^{2} ( x )}{cos ^{2} ( x ) sin ^{2} ( x )}

Factor

cos^{4} (x) + sin^{4} (x) + 2 cos^{2} (x) sin^{2} (x) : (sin^{2} (x) + cos^{2} (x))^{2}

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

Rewrite using trig identities

= csc^{2} (x) sec^{2} (x)

\frac{( 1 - i ) ^{15}}{128}

(9 sin (x) - 1) (9 sin (x) + 1)

3 (5 + 6)

x^{2} (\frac{1}{x} - \frac{1}{y})

\frac{9 x ^{2} - 9 x + 6}{( x - 1 ) ( 2 x - 1 ) ( x + 2 )}

What is expand (cot(x)+tan(x))^2 ?
The solution to expand (cot(x)+tan(x))^2 is csc^2(x)sec^2(x)