what is the maximum value of 3 - 7cos5x......plz give solution
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max value is 11 . . . .
abhishek088:
ans is 10 and plz give solution
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we have to find maximum value of (3 - 7cos5x)
we know, cosine function lies between -1 to 1
e.g., - 1 ≤ cos5x ≤ 1
multiplying with 7,
-7 ≤ 7cos5x ≤ 7
multiplying (-1), then, sign will be change of inequality.
(-1)(-7) ≥ (-1)7cos5x ≥ (-1)7
7 ≥ -7cos5x ≥ -7
now adding 3,
7 + 3 ≥ 3 - 7cos5x ≥ 3 - 7
10 ≥ 3 - 7cos5x ≥ - 4
or, -4 ≤ (3 - 7cos5x) ≤ 10
hence, maximum value of (3 - 7cos5x) = 10
we know, cosine function lies between -1 to 1
e.g., - 1 ≤ cos5x ≤ 1
multiplying with 7,
-7 ≤ 7cos5x ≤ 7
multiplying (-1), then, sign will be change of inequality.
(-1)(-7) ≥ (-1)7cos5x ≥ (-1)7
7 ≥ -7cos5x ≥ -7
now adding 3,
7 + 3 ≥ 3 - 7cos5x ≥ 3 - 7
10 ≥ 3 - 7cos5x ≥ - 4
or, -4 ≤ (3 - 7cos5x) ≤ 10
hence, maximum value of (3 - 7cos5x) = 10
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