# Trig

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sin^4t-cos^4t/sin^2t cos^2t= sec^2t-csc^2t

i have =(sin^2t+cos^2t)(sin^2t+cos^2t)/sin^2tcos^2t
then do i go =(sin^2t+cos^2t)/sin^2tcos^2t

stumped

• Trig -

LS = (sin^2 t + cos^2 t)(sin^2 t - cos^2 t)/(sin^2 t cos^2 t)
= 1(sin^2 t - cos^2 t)/(sin^2 t cos^2 t)
= sin^2 t/(sin^2 t cos^2 t) - cos^2 t/(sin^2 t cos^2 t)
= 1/cos^2 t - 1/sin^2 t
= sec^2 t - csc^2 t
= RS

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