1
Question
cosec6A - cot 6A = 3 cot2A * cosec2A +1
Emergency. PROVE LHS = RHS
Emergency. PROVE LHS = RHS
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Solution
LHS=
=>cosec^2 A) ^3 - (cot^2A)^3 =
=>(cosec^2A - cot^2 A)^ 3 +
=>3( cosec^2A.cot^2A)( cosec^2A - cot^2A)
=>1^3+3( cosec^2A.cot^2A)( cosec^2A - cot^2A)
==>1 + 3 ( cosec^2A*cot^2A).
=RHS
( Use formula ; a^3 - b ^3 = ( a - b ) ^3 + 3 ab( a - b )
(cosec^2A - cot^2 A)=1
=>cosec^2 A) ^3 - (cot^2A)^3 =
=>(cosec^2A - cot^2 A)^ 3 +
=>3( cosec^2A.cot^2A)( cosec^2A - cot^2A)
=>1^3+3( cosec^2A.cot^2A)( cosec^2A - cot^2A)
==>1 + 3 ( cosec^2A*cot^2A).
=RHS
( Use formula ; a^3 - b ^3 = ( a - b ) ^3 + 3 ab( a - b )
(cosec^2A - cot^2 A)=1
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