2sec²theta-2cosec²theta-sec⁴theta+coesc⁴theta=cot⁴theta-tan⁴theta
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Step-by-step explanation:
Let theta be A.
2sec²A-2cosec²A-sec⁴A+cosec⁴A=cot⁴A-tan⁴A.
LHS=2sec²A-2cosec²A-sec⁴A+cosec⁴A
=2+2tan²A-2-2cot²A-1-tan⁴A+1+cot⁴A
[sec²A=1+tan²A, cosec²A=1+cot²A]
=2tan²A-2cot²A-(-(tan⁴A+cot⁴A))
[ take (-) common]
=(tan²A-cot²A)(2-2-cot⁴A+tan⁴A)
=(tan²A-cot²A)(tan²A-cot²A)
=-(tan⁴A-cot⁴A)
=cot⁴A-tan⁴A
=RHS
LHS=RHS.
Hope helps u.
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