What is (tan(x^3+pi/4))^2 ?

The solution to (tan(x^3+pi/4))^2 is (1+sin(2x^3))/(1-sin(2x^3))

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simplify (tan(x^3+pi/4))^2

simplify

(tan (x^{3} + \frac{π}{4}))^{2}

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

Solution steps

tan^{2} (x^{3} + \frac{π}{4})

Rewrite using trig identities

= (\frac{sin ( x ^{3} ) + cos ( x ^{3} )}{cos ( x ^{3} ) - sin ( x ^{3} )})^{2}

Apply exponent rule:

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

= \frac{( sin ( x ^{3} ) + cos ( x ^{3} ) ) ^{2}}{( cos ( x ^{3} ) - sin ( x ^{3} ) ) ^{2}}

Expand

\frac{( cos ( x ^{3} ) + sin ( x ^{3} ) ) ^{2}}{( cos ( x ^{3} ) - sin ( x ^{3} ) ) ^{2}} : \frac{cos ^{2} ( x ^{3} ) + 2 cos ( x ^{3} ) sin ( x ^{3} ) + sin ^{2} ( x ^{3} )}{cos ^{2} ( x ^{3} ) - 2 cos ( x ^{3} ) sin ( x ^{3} ) + sin ^{2} ( x ^{3} )}

= \frac{cos ^{2} ( x ^{3} ) + sin ^{2} ( x ^{3} ) + 2 cos ( x ^{3} ) sin ( x ^{3} )}{cos ^{2} ( x ^{3} ) + sin ^{2} ( x ^{3} ) - 2 cos ( x ^{3} ) sin ( x ^{3} )}

Rewrite using trig identities

= \frac{1 + sin ( 2 x ^{3} )}{1 - sin ( 2 x ^{3} )}

sin (aπ + \frac{π}{3})

sin (\frac{π}{6} + x)

64 - (8 sin (θ))^{2}

- cos (x - 123 π)

e^{- l n (c o s (x)) + c}

What is (tan(x^3+pi/4))^2 ?
The solution to (tan(x^3+pi/4))^2 is (1+sin(2x^3))/(1-sin(2x^3))