ICSE Class 11-science Answered
Prove that : Sec^6x-tan^6x= 1+3tan^2x+ 3tan^4x
Asked by siddharthlathia0 | 10 Jun, 2018, 06:55: AM
Expert Answer
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a³-b³=(a-b)³+3ab(a-b)
1+tan²x=sec²x
(sec²x)³-(tan²x)³=(sec²x-tan²x)³+3sec²xtan²x(sec²x-tan²x)
=1³+3sec²xtan2x(1)
=1+3tan²xsec²x
1+tan²x=sec²x
(sec²x)³-(tan²x)³=(sec²x-tan²x)³+3sec²xtan²x(sec²x-tan²x)
=1³+3sec²xtan2x(1)
=1+3tan²xsec²x
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