SOLUTION: Verify that the equation is an identity. tan^2S*sin^2S = tan^2S+ cos^2S

SOLUTION: Verify that the equation is an identity. tan^2S*sin^2S = tan^2S+ cos^2S - 1

Question 173675This question is from textbook Trigonometry
: Verify that the equation is an identity.
tan^2S*sin^2S = tan^2S+ cos^2S - 1 This question is from textbook Trigonometry

Answer by SAT Math Tutor(36) (Show Source): You can put this solution on YOUR website!
You need to use the following identity twice:
sin^2(s) + cos^2(s) = 1
OR sin^2(s) = 1 - cos^2(s)
OR cos^2(s) = 1 - sin^2(s)
Start by replacing sin^2(s) with 1 - cos^2(s) on the left hand side of the equation:
tan^2(s)*(1-cos^2(s)) = tan^2(s) + cos^2(s) - 1
Then, distribute:
tan^2(s) - tan^2(s)*cos^2(s) = tan^2(s) + cos^2(s) - 1
Since tan^2(s) = , simplify the left hand side to:
tan^2(s) - sin^2(s) = tan^2(s) + cos^2(s) - 1
Then, replace cos^2(s) with 1 - sin^2(s) on the right hand side:
tan^2(s) - sin^2(s) = tan^2(s) + 1 - sin^2(s) - 1
tan^2(s) - sin^2(s) = tan^2(s) - sin^2(s)
So they are equal!
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