(sin^6 x)/(1- tan^2 x) + (cos^6 x)/(1- cot^2 x)

Question

simplify simplify simplify simplify ...............

Answer 1

 

(sin^6 x)/(1-tan^2 x) + (cos^6 x)/(1-cot^2 x)

= sin^6 x/(1 - sin^2 x/cos^2 x) + cos^6 x/(1 - cos^2 x/sin^2 x)

= sin^6 x cos^2 x/(cos^2 x - sin^2 x) + cos^6 x sin^2 x/(sin^2 x - cos^2 x)

= sin^2 x cos^2 x (sin^4 x - cos^4 x)/(cos^2 x - sin^2 x)

= sin^2 x cos^2 x (sin^2 x - cos^2 x)(sin^2 x + cos^2 x)/(cos^2 x - sin^2 x)

= -sin^2 x cos^2 x <==Answer

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Attn:

sin^2 x + cos^2 x = 1