SOLUTION: Verify that the equation is an identity {{{(cot^2(x) - tan^2(x)) / (cot^""(x)^"" + tan^""(x))^2}}}{{{""=""}}}{{{2cos^2(x)-1}}}

Question 1012353: Verify that the equation is an identity

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!



Work with the left side. Factor the numerator as the difference
of two squares.
Write the denominator as the product of 
two equal factors:


Cancel:





Use the quotient identities to change everything to sines
and cosines:



Multiply top and bottom by LCD = sin(x)cos(x)



Use the Pythagorean identity to replace the bottom by 1:





Use the Pythagorean identity to change the sin²(x)







Edwin

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