Question

Prove that
Cosec⁶ A =Cot⁶A+3Cot²ACosec²A+1​

Answer 1

see figure in attachment...

hope it's helpful to you

Answer 2

Answer:

$\huge{ \underline{ \rm{ \large { \pink{Prove:}}}}}$

• ${ \sf{ {Cosec}^{6} A = {Cot}^{6} A + 3 {Cot}^{2}A {Cosec}^{2} A}}$

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Given LHS ⇒ Cosec⁶A

$\: \: \:$

${ \implies{ \sf{ {( {Cosec}^{2}A) }^{3} }}}$

From identity ⤵

$\: \: \: \: \: { \boxed{ \sf{1 + {Cot}^{2} A = {Cosec}^{2} A}}}$

${ \implies{ \sf{ {( {1 + Cot}^{2}A) }^{3} }}}$

${ \boxed{ \green{ \sf{( {a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) }}}}$

${ \implies{ \sf{1 + {( {Cot}^{2} A)}^{3} + 3 {Cot}^{2} A(1 + {Cot}^{2} A) }}}$

${ \implies{ \sf{1 + {Cot}^{6}A + 3 {Cot}^{2}A {Cosec}^{2} A + {Cot}^{2} A }}}$

LHS = RHS

Hence proved