Prove that sin⁶x + cos⁶x = 1 - 3 sin²x cos²x

Evaluate tan 480⁰

Prove that \(\frac { cos(2\pi +x)cosec(2\pi +x)tan\left( \frac { \pi }{ 2 } +x \right) }{ sec\left( \frac { \pi }{ 2 } +x \right) cos.cot(\pi +x) } \)= 1

Find the value of tan\(\frac { \pi }{ 2 } \).

Prove that \(\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x } \)