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

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

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

simplify

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

1

Solution steps

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

\frac{1}{1 + tan ^{2} ( x )} = \frac{1}{sec ^{2} ( x )}

\frac{1}{1 + cot ^{2} ( x )} = \frac{1}{csc ^{2} ( x )}

= \frac{1}{sec ^{2} ( x )} + \frac{1}{csc ^{2} ( x )}

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

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

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

Use the Pythagorean identity:

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

= 1

\frac{5}{x + 9} + \frac{5}{x}

4 y

- 10 (1 - 9 x) + 6 (x - 10)

\frac{m ^{2} - 9}{9 m - m ^{3}}

- 1 + (- 6)

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