Question

cosec6@-cot6@=1+3cosec2@cot2@

Answer 1

more detail contect 8890085771

Answer 2

Proving L.H.S=R.H.S

Step-by-step explanation:

Given that:

$(cosec @)^6-(cot @)^6=1+3(cosec @)^2(cot @)^2$

$Solving\ L.H.S\ part:$

$(cosec \ @)^6-(cot \ @)^6$

$formula: \ (a)^3-(b)^3= (a-b)((a)^2+ab+(b)^2)$

$((cosec \ @)^2)^3-((cot \ @)^2)^3$=

$((cosec \ @)^2-(cot \ @)^2)((cosec \ @^2)^2+(cot \ @^2)^2+(cosec \ @)^2\cdot (cot \ @)^2)$

$\therefore cosec^2 \theta -cot^2 \theta \ = \ 1$

$(1).((cosec \ @^2)^2+(cot \ @^2)^2+(cosec \ @)^2\cdot (cot \ @)^2)$

$formula:\ (a-b)^2=(a)^2+(b)^2-2 \cdot a \cdot b$

$\therefore (a)^2+(b)^2= (a-b)^2+2 \cdot a \cdot b$

$(cosec \ @^2)^2+(cot \ @^2)^2=(((cosec \ @^2)-(cot \ @^2))^2+2(cosec \ @)^2\cdot (cot \ @)^2+)$

$(cosec \ @^2)^2+(cot \ @^2)^2=((1)^2+3(cosec \ @)^2\cdot (cot \ @)^2)$

$((1)^2+3(cosec \ @)^2(cot \ @)^2)$

$(1+3cosec^2 \ @.cot^2 \ @)$

L.H.S=R.H.S

Learn more:

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