Question

please help me guys​

Answer 1

Step-by-step explanation:

Sec^6 x - tan^6 x = 1+3sec^2 x * tan^2 x

use property :-

(a-b)^3 = a^3 - b^3 - 3ab(a-b)

a^3-b^3 = (a-b)^3 + 3ab(a-b)

let's assume :

Sec^2 x = A

Tan^2 x = B

take LHS Step :

A^3 - B^3 = (Sec^2 x)^3 - (tan^2 x )^3

(Sec^2 x - tan^2 x)^3 + 3(sec^2 x)(tan^2 x)(sec^2 x - tan^2 x)

we know that : sec^2 - tan^2 = 1

(1)^3 + 3(sec^2 x)(tan^2 x)(1)

= 1 + 3(sec^2 x)(tan^2 x)

so LHS = RHS

hence prooved !!