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27/12/2021 12:00 pm
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If f(x) = cos[2tan-1(sin(cot-1\sqrt{\frac{1-x}{x}}))]
(a) f'(x)(x-1)2 - 2(f(x))2 = 0
(b) f'(x)(x-1)2 + 2(f(x))2 = 0
(c) f'(x)(x+1)2 + 2(f(x))2 = 0
(d) f'(x)(x+1)2 - 2(f(x))2 = 0
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27/12/2021 12:10 pm
Correct answer: (c) f'(x)(x+1)2 + 2(f(x))2 = 0
Explanation:
f(x) = cos\Big[2tan^{-1}\Big( sin \Big( cot^{-1}\sqrt{\frac{1-x}{x}}\Big) \Big) \Big]
= cos (2tan-1√x)
= \Big(\frac{2}{1 + x}\Big) - 1
∴ f'(x) = \frac{-2}{(1 -x)^2}
⟹ f'(x)(x+1)2 = -2
This post was modified 3 years ago 6 times by Reyana09