The left hand side of the equation contains tan raised to the power of 4 and 2.tan^4(x) + tan^2(x) = sec^4(x) - sec^2(x)

**can be written as**

*tan^4(x)**, so the left hand side can be written as:*

**(tan^2(x))^2**From the identity(tan^2(x))^2 + tan^2(x)

*, it follows that*

**1 + tan^2(x) = sec^2(x)***.*

**tan^2(x) = sec^2(x) - 1**Apply the algebraic identity(sec^2(x) - 1)^2 + sec^2(x) - 1

*to*

**(a - b)^2 = a^2 + b^2 - 2ab**

**(sec^2(x) - 1)^2**Simplify by adding like terms.sec^4(x) + 1 - 2sec^2(x) + sec^2(x) - 1

... which is the right hand side of the equationsec^4(x) - sec^2(x)

Trigonometric identities applied: