What is ((1+cot^2(a)))/((1+tan^2(a))) ?

The solution to ((1+cot^2(a)))/((1+tan^2(a))) is cot^2(a)

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simplify ((1+cot^2(a)))/((1+tan^2(a)))

simplify

\frac{( 1 + cot ^{2} ( a ) )}{( 1 + tan ^{2} ( a ) )}

cot^{2} (a)

Solution steps

\frac{1 + cot ^{2} ( a )}{1 + tan ^{2} ( a )}

Simplify

1 + cot^{2} (a) : csc^{2} (a)

= \frac{csc ^{2} ( a )}{1 + tan ^{2} ( a )}

Simplify

1 + tan^{2} (a) : sec^{2} (a)

= \frac{csc ^{2} ( a )}{sec ^{2} ( a )}

Use the basic trigonometric identity:

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

= csc^{2} (a) cos^{2} (a)

Express with sin, cos

= \frac{cos ^{2} ( a )}{sin ^{2} ( a )}

Rewrite using trig identities

= cot^{2} (a)

3 cos^{2} (x) - 3

\frac{( 18 x ^{2} - 21 x )}{( 6 x - y )}

a (a - 1) x^{2} + (2 a^{2} - 1) x + a (a + 1)

(x - 2 y) + (2 y - 3 z) 3 + (3 z - x) 3

\frac{2}{3} \cdot (- b + a) + b

What is ((1+cot^2(a)))/((1+tan^2(a))) ?
The solution to ((1+cot^2(a)))/((1+tan^2(a))) is cot^2(a)