Asked by Mb
Demostrate the validity of tan^2theta-sin^2theta=sin^4theta sec^2theta
Answers
Answered by
Reiny
tan^2 Ø - sin^2 Ø = sin^4 Ø sec^2 Ø
LS = sin^2 Ø/cos^2 Ø - sin^2 Ø
= (sin^2 Ø - sin^2 Ø cos^2 Ø)/cos^2 Ø , using a common denominator.
= (sin^2 Ø - sin^2 Ø(1 - sin^2 Ø)/cos^2 Ø
= (sin^2 Ø - sin^2 Ø + sin^4 Ø)/cos^2 ‚
= sin^4 Ø sec^2 Ø
= RS
LS = sin^2 Ø/cos^2 Ø - sin^2 Ø
= (sin^2 Ø - sin^2 Ø cos^2 Ø)/cos^2 Ø , using a common denominator.
= (sin^2 Ø - sin^2 Ø(1 - sin^2 Ø)/cos^2 Ø
= (sin^2 Ø - sin^2 Ø + sin^4 Ø)/cos^2 ‚
= sin^4 Ø sec^2 Ø
= RS
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