Write an identity in terms of sines and cosines to simplify it. The .pdf
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The document discusses simplifying an expression involving trigonometric identities, specifically 1 + cot²x / 1 - csc²x. It outlines the steps to rewrite cotangent and cosecant in terms of sine and cosine, ultimately simplifying the expression to -sec²x. The final result is presented as an option: -sec²x.
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Write an identity in terms of sines and cosines to simplify it. The .pdf
- 1. Write an identity in terms of sines and cosines to simplify it. The expression 1 + cot^2 x/1 - CSC^2 x simplifies to sin x cos x 1 - cos^2 x tan^2 x + 1 -sec^2z sin x tan x sec x Solution (1+cot^2x)/( 1-csc^2x) we know cotx = cosx/sinx ; cscx = 1/sinx (1+cot^2x)/( 1-csc^2x) = ( cos^2x +sin^2x)/(sin^2x -1) =1/(-cos^2x) = -sec^2x OPtion : -sec^2x