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Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as?
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Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minu...
The given expression is log(1/(1/(1-x^2)^(1-1/2))). We can simplify this expression using the following steps:
1. Simplify the expression inside the parentheses:
(1-x^2)^(1-1/2) = (1-x^2)^(1/2-1) = 1/sqrt(1-x^2)
2. Substitute this simplified expression into the original expression:
log(1/(1/(1-x^2)^(1-1/2))) = log(1/(1/(1-x^2)^(1/2-1))) = log(1/(1/sqrt(1-x^2)))
3. Use the logarithmic identity log(a/b) = log(a) - log(b) to simplify the expression further:
log(1/(1/sqrt(1-x^2))) = log(1) - log(1/sqrt(1-x^2)) = -log(1/sqrt(1-x^2))
4. Simplify the expression inside the logarithm:
1/sqrt(1-x^2) = (1-x^2)^(-1/2) = sec(x)
5. Substitute this simplified expression into the previous expression:
-log(1/sqrt(1-x^2)) = -log(sec(x)) = -ln|sec(x) + tan(x)| + C
where C is a constant of integration.
Therefore, the given expression can be written as -ln|sec(x) + tan(x)| + C.
1. Simplify the expression inside the parentheses:
(1-x^2)^(1-1/2) = (1-x^2)^(1/2-1) = 1/sqrt(1-x^2)
2. Substitute this simplified expression into the original expression:
log(1/(1/(1-x^2)^(1-1/2))) = log(1/(1/(1-x^2)^(1/2-1))) = log(1/(1/sqrt(1-x^2)))
3. Use the logarithmic identity log(a/b) = log(a) - log(b) to simplify the expression further:
log(1/(1/sqrt(1-x^2))) = log(1) - log(1/sqrt(1-x^2)) = -log(1/sqrt(1-x^2))
4. Simplify the expression inside the logarithm:
1/sqrt(1-x^2) = (1-x^2)^(-1/2) = sec(x)
5. Substitute this simplified expression into the previous expression:
-log(1/sqrt(1-x^2)) = -log(sec(x)) = -ln|sec(x) + tan(x)| + C
where C is a constant of integration.
Therefore, the given expression can be written as -ln|sec(x) + tan(x)| + C.
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Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as?
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Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as?.
Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Log of 1 - of 1 - of 1 - x square whole power minus 1 whole power minus 1 whole power minus 1 by 2 can be written as?.
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