How do you prove # 1/sec^2 x + 1/csc^2 x =1#?

1 Answer
Mar 3, 2018

# 1/csc^(2⁡)x +1/sec^(2)x =1#

#1/(1/sin^(2⁡)x )+1/(1/cos^(2⁡)x )=1#

# sin^2⁡x+cos^2⁡x=1#

# 1=1#

Explanation:

  1. Use reciprocal identity to transform #1/csc^2 x# and #1/sec^2 x# to #1/[1/ (sin^2 x)]# and #1/[1/(cos^2 x)]# respectively.

  2. Reciprocate #sin^2 x# and #1/(cos^2 x)# you will get #sin^2x# and #cos^2 x#, respectively.

  3. #sin^2⁡x+cos^2⁡x# is equal to #1# by the Pythagorean Fundamental Identity.