Question

prove that sec^6=tan^6+3tan²sec²+1​

Answer 1

Step-by-step explanation:

Sec^6 = ( Sec^2 ) ^3

= ( 1 + Tan^2 ) ^3

= Tan^6 + 1 + Tan^2 ( 1+Tan^2)

= Tan^6 +1 + Tan^2 . Sec^2

Answer 2

$\mathfrak{here \: is \: your \: answer} \\ {sec}^{6} = tan { }^{6} + 3tan {}^{2} sec {}^{2} + 1 \\ \blue{ {sec}^{6}=( sec {}^{2}) {}^{3} } \\ \blue{{sec}^{6} = (1 + tan {}^{2}) {}^{3} } \\ \blue{{sec}^{6} = 1 + tan {}^{6} + 3tan {}^{2} + 1}$

Hope my answer will help you.