What is (1+tan^2(x))^{3/2} ?

The solution to (1+tan^2(x))^{3/2} is sec^3(x)

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simplify (1+tan^2(x))^{3/2}

simplify

(1 + tan^{2} (x))^{\frac{3}{2}}

sec^{3} (x)

Solution steps

(1 + tan^{2} (x))^{\frac{3}{2}}

Use the Pythagorean identity:

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

= (sec^{2} (x))^{\frac{3}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= sec^{2 \cdot \frac{3}{2}} (x)

2 \cdot \frac{3}{2} = 3

= sec^{3} (x)

sin (- t) \cdot sec (t) - tan (- t)

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sin (- 2 t) - sin (2 t)

4 tan^{2} (x) + 4

sec (arctan (u))