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Draw the graph of f(x) = (sin x)/(sqrt(1 + tan^(2)x))- (cos x)/(sqrt(1 + cot^(2)x)). Then find the range of f(x). |
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Answer» SOLUTION :`f(x) = (SIN x)/(|sec x|) - (cos x)/(|"cosec "x|)` `= sin x *| cos x| - cos x * |sin x|` `= {{:(0",", x in (0", "pi//2)),(-sin 2x, x in (pi//2, pi)),(0",", x in (pi, 3pi//2)),(sin 2x",", x in (3pi//2, 2pi)):}` Clearly the domain of f(x) is `R - {(NPI)/(2), nin Z}` and the PERIOD of f(x) is `2pi`. So the range of f(x) is (-1, 1).
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