Verify the identity 3 minus 3 tan4xsec2x 31 minus tan2x Fir

Verify the identity. 3 minus 3 tan^4x/sec^2x = 3(1 minus tan^2x) First factor the numerator, then use the Pythagorean identity for sec^2x. Finally simplify by dividing out the common factors. (Simplify completely at each step.) 3 minus 3 tan^4x/sec^2 x = 3(1 minus tan^4 x)/sec^2 x = 3(1 + tan^2 x)(1 minus tan^2 x)/sec^2 x = 3()(1 minus tan^2 x)/sec^2x =1 minus tan x + tan^2 x Verify the identity. 1 + tan^3 x/1 + tan x = 1 minus tan x + tan^2 x Factor the numerator, and then simplify by dividing out the common factors.

Solution

(3 - 3tan^4x)/sec^2x

= 3( 1- tan^4x)/sec^2x

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

= 3*sec^2x(1- tan^2x)/sec^2x

= 3(1-tan^2x)

= RHS