Question

2sec²theta-2cosec²theta-sec⁴theta+coesc⁴theta=cot⁴theta-tan⁴theta

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Answer 1

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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Answer 2

Answer:

answer attached in photo