Cos^4 (50°) - cos^4 (40°) equal ?

1 Answer
Sep 24, 2017

#cos100^@=-cos80^@=-sin10^@.#

Explanation:

We know that, # (1) : costheta=sin(90^@-theta), and, #

# (2) : cos^2theta-sin^2theta=cos2theta.#

By #(1), cos40^@=sin50^@.#

#:. cos^4 50^@-cos^4 40^@,#

#=cos^4 50^@-sin^4 50^@.#

Since, #a^2-b^2=(a+b)(a-b),# we get,

#"The Exp.="(cos^2 50^@+sin^2 50^@)(cos^2 50^@-sin^2 50^@),#

#=(1)(cos(2xx50^@),#

#=cos100^@.#

#because, cos(180^@-theta)=-costheta,# we have the other

equvalent Answers are, #-cos80^@=-sin10^@.#