Question
If 2x = cosec @ and 4/x = cot @ then the value of 2(x Ā²
- 1/x Ā² ) isSolution
2x = cosec@ .............(i) 2/x = cotĀ @ ...............(ii) adding (i) and (ii), we get 2 (x + 1/x) = cosecĀ @ + cotĀ @ ...........(iii) subtracting (ii) from (i), we get 2 (x - 1/x) = cosecĀ @ - cotĀ @ ..............(iv) Multiply (iii) and (iv), we get 4 (x 2Ā Ā - 1/x2) = cosec2Ā Ā @ - cot 2 Ā @Ā 2(x2Ā Ā - 1/x2Ā Ā ) = 1/2Ā
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