Question #f183d
1 Answer
Jan 29, 2018
the expression is an identity
Explanation:
We seek to determine if the following is an identity:
# (1-tan^2x)/(sec^2x) = cos^2x - 1/(csc^2x) #
Consider the LHS:
# LHS = (1-tan^2x)/(sec^2x) #
# \ \ \ \ \ \ \ \ = (1-sin^2x/cos^2x)/((1/cos^2x)) #
# \ \ \ \ \ \ \ \ = (1-sin^2x/cos^2x) * (cos^2x) #
# \ \ \ \ \ \ \ \ = cos^2x-sin^2x #
# \ \ \ \ \ \ \ \ = cos^2x-1/(1/sin^2x) #
# \ \ \ \ \ \ \ \ = cos^2x-1/(csc^2x) \ \ \ #
Confirm that the expression is an identity
