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

The solution to 1+tan^2(pi/2-x) is csc^2(x)

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simplify 1+tan^2(pi/2-x)

simplify

1 + tan^{2} (\frac{π}{2} - x)

csc^{2} (x)

Solution steps

1 + tan^{2} (\frac{π}{2} - x)

Rewrite using trig identities

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Rewrite using trig identities

= csc^{2} (x)

- sin (x - \frac{π}{2})

cos (arcsin (17 x))

tan (arcsec (\frac{x}{8}))

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

tan (arccos (\frac{x}{4}))