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Question
cosec4θ − cosec2θ = cot4θ + cot2θ
Solution 1
LHS = cosec4θ − cosec2θ
LHS = cosec2θ (cosec2θ − 1)
`"LHS" = (cot^2θ + 1)cot^2θ ...{(cot^2θ + 1 = cosec^2θ),(∵ cot^2θ = cosec^2θ - 1):}`
LHS = cot4θ + cot2θ
RHS = cot4θ + cot2θ
RHS = LHS
Hence proved.
Solution 2
RHS = cot4θ + cot2θ
RHS = cot2θ (cot2θ + 1)
`"RHS"=(cosec^2θ-1)cosec^2θ ...{(cot^2θ+1=cosec^2θ),(∵ cot^2θ=cosec^2θ-1):}`
RHS = cosec4θ − cosec2θ
LHS = cosec4θ − cosec2θ
RHS = LHS
Hence proved.
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