How do you verify #sec^2(x)+csc^2(x)=(sec(x)csc(x))^2#?

1 Answer
Alan P.
Jul 1, 2015

Use the inverse forms of sec and csc; apply rule #sin^2+cos^2 = 1# and perform standard algebraic operations.

Explanation:

#sec^2(x)+csc^2(x)#
#color(white)("XXXX")##=1/(cos^2(x)) + 1/(sin^2(x))#

#color(white)("XXXX")##=(sin^2(x)+cos^2(x))/(cos^2(x)*sin^2(x))#

#color(white)("XXXX")##=1/(cos^2(x)*sin^2(x))#

#color(white)("XXXX")##=1/cos^2(x)*1/sin^2(x)#

#color(white)("XXXX")##= sec^2(x) * csc^2(x)#

#color(white)("XXXX")##= (sec(x)csc(x))^2#

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