What is (sec^2(pix)-1)^3 ?

The solution to (sec^2(pix)-1)^3 is tan^6(pix)

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simplify (sec^2(pix)-1)^3

simplify

(sec^{2} (π x) - 1)^{3}

tan^{6} (π x)

Solution steps

(sec^{2} (π x) - 1)^{3}

Use the Pythagorean identity:

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

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

= (tan^{2} (π x))^{3}

Apply exponent rule:

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

= tan^{2 \cdot 3} (π x)

Multiply the numbers:

2 \cdot 3 = 6

= tan^{6} (π x)

cos (3 x + 3 π)

tan (x - \frac{π}{6}) - 1

tan (\frac{π}{4} - arctan (x))

csc (\frac{π}{2} - θ)

cos (\frac{π}{2} + π \frac{n}{2})