How do you verify the identity #secx-cos^2xcscx=tanxsecx#?

2 Answers
Nov 22, 2016

This equation is not correct if you pick a value for x say #pi/3#and plug it in to both sides then you can see that it is not a true statement.

Nov 22, 2016

The equation is not true.

Explanation:

Check if the equation is true or not by computing the left side, then the right side:

Left Side:
#secx-cos^2xcscx#
#=1/cosx-cos^2x/sinx#
#=frac{sinx-cos^2xcosx}{cosxsinx}#
#=frac{sinx-cos^3x}{cosxsinx}#

Right Side:
#tanxsecx#
#=sinx/cosx*1/cosx#
#=sinx/cos^2x#

The equation above is not true because the left side of the equation is not equal to the right side of the equation:
#frac{sinx-cos^3x}{cosxsinx}cancel(=)sinx/cos^2x#