Find the minimum value of 2 cosec^2x -4 cosec
x +9
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Answer:
minimum value of of 2Cosec²x - 4Cosecx + 9 = 7
Step-by-step explanation:
2Cosec²x - 4Cosecx + 9
= 2(Cosec²x - 2Cosecx + 9/2)
= 2(Cosec²x - 2Cosecx + 1 - 1 + 9/2)
= 2(Coseex - 1)² + 2(9/2 - 1)
= 2(Coseex - 1)² + 9 - 2
= 2(Cosecx - 1)² + 7
(Cosecx - 1)² can not be - ve
Hence minimum value of of 2Cosec²x - 4Cosecx + 9 = 7
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