What is expand (1+tan^4(t/(12)))^3 ?

The solution to expand (1+tan^4(t/(12)))^3 is 1+3tan^4(t/(12))+3tan^8(t/(12))+tan^{12}(t/(12))

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expand (1+tan^4(t/(12)))^3

expand

(1 + tan^{4} (\frac{t}{12}))^{3}

1 + 3 tan^{4} (\frac{t}{12}) + 3 tan^{8} (\frac{t}{12}) + tan^{12} (\frac{t}{12})

Solution steps

(1 + tan^{4} (\frac{t}{12}))^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + tan^{4} (\frac{t}{12}))^{3} = 1^{3} + 3 \cdot 1^{2} tan^{4} (\frac{t}{12}) + 3 \cdot 1 \cdot (tan^{4} (\frac{t}{12}))^{2} + (tan^{4} (\frac{t}{12}))^{3}

= 1^{3} + 3 \cdot 1^{2} tan^{4} (\frac{t}{12}) + 3 \cdot 1 \cdot (tan^{4} (\frac{t}{12}))^{2} + (tan^{4} (\frac{t}{12}))^{3}

1^{3} = 1

3 \cdot 1^{2} tan^{4} (\frac{t}{12}) = 3 tan^{4} (\frac{t}{12})

3 \cdot 1 \cdot (tan^{4} (\frac{t}{12}))^{2} = 3 tan^{8} (\frac{t}{12})

(tan^{4} (\frac{t}{12}))^{3} = tan^{12} (\frac{t}{12})

= 1 + 3 tan^{4} (\frac{t}{12}) + 3 tan^{8} (\frac{t}{12}) + tan^{12} (\frac{t}{12})

(t - \frac{1}{2}) (t^{2} - t + \frac{1}{6})

\frac{1}{( x + y i ) ^{2} - 4}

- cos (v) sin (u) (2 cos (v) + cos (v) cos (u))

(1 + t) (- \frac{1}{2} ((t + 1)^{2} - t^{2}))

(sin (2 t) + 2 sin (t)) \cdot (2 sin (t) - 2 sin (2 t))

What is expand (1+tan^4(t/(12)))^3 ?
The solution to expand (1+tan^4(t/(12)))^3 is 1+3tan^4(t/(12))+3tan^8(t/(12))+tan^{12}(t/(12))