Question

verify the identity. show all work. sin^4theta-cos^4theta=sin^2theta-cos^2theta

Answer 1

have u tried this ?

Answer 2

no idk how to start

Answer 3

write sin^4 theta = (sin^2 theta )^2
same for cos^4 theta
what u get ?

Answer 4

sin ^2 theta^2 -cos^theta^2

Answer 5

yesh, now use
\(a^2-b^2=(a+b)(a-b)\)
with a=sin^2 theta, b= cos^2 theta

Answer 6

so sin^theta + cos^2theta(sin^2theta-cos^2theta)

Answer 7

yeah, don't miss out brackets , (sin^2 theta + cos^2 theta)(sin^2theta-cos^2theta)
and i think you know what is (sin^2 theta + cos^2 theta) = ?

Answer 8

theta right ? or is it 1

Answer 9

\(\huge \color{red}{sin^2x+cos^2x = 1}\)

Answer 10

so its 1, so what remains ?

Answer 11

sin ^2 theta -cos^2theta which is equal to the rhs (:

Answer 12

yes, thats it :) clear with all steps ?

Answer 13

yea thank you so much ur a great help

Answer 14

welcome ^_^