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. If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .?
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. If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x...
Given Information:
- 3x = cosec θ
- 3/x = cot θ
Calculating the value of 3(x^2 - 1/(x^2)):
Finding the value of x:
Since 3x = cosec θ, x = 1/3cosec θ = 1/(3sin θ)
Finding the value of 1/x:
Since 3/x = cot θ, 1/x = 3cot θ = 3/tan θ = 3/(sin θ/cos θ) = 3cos θ/sin θ = 3cosec θ
Calculating the value of 3(x^2 - 1/(x^2)):
Substitute the values of x and 1/x into the expression:
3[(1/(3sin θ))^2 - 1/(3cosec θ)^2]
= 3[(1/(9sin^2 θ)) - 1/(9/sin^2 θ)]
= 3[(1/(9sin^2 θ)) - sin^2 θ/9]
= 3[(1 - sin^4 θ)/(9sin^2 θ)]
= (3 - 3sin^4 θ)/(9sin^2 θ)
= (3(1 - sin^4 θ))/(9sin^2 θ)
= (3cos^4 θ)/(9sin^2 θ)
= cos^4 θ/(3sin^2 θ)
- 3x = cosec θ
- 3/x = cot θ
Calculating the value of 3(x^2 - 1/(x^2)):
Finding the value of x:
Since 3x = cosec θ, x = 1/3cosec θ = 1/(3sin θ)
Finding the value of 1/x:
Since 3/x = cot θ, 1/x = 3cot θ = 3/tan θ = 3/(sin θ/cos θ) = 3cos θ/sin θ = 3cosec θ
Calculating the value of 3(x^2 - 1/(x^2)):
Substitute the values of x and 1/x into the expression:
3[(1/(3sin θ))^2 - 1/(3cosec θ)^2]
= 3[(1/(9sin^2 θ)) - 1/(9/sin^2 θ)]
= 3[(1/(9sin^2 θ)) - sin^2 θ/9]
= 3[(1 - sin^4 θ)/(9sin^2 θ)]
= (3 - 3sin^4 θ)/(9sin^2 θ)
= (3(1 - sin^4 θ))/(9sin^2 θ)
= (3cos^4 θ)/(9sin^2 θ)
= cos^4 θ/(3sin^2 θ)
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. If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .?
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. If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about . If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .?.
. If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about . If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . If 3x = cosec 0 and 3/x = cot theta find the value of 3(x ^ 2 - 1/(x ^ 2)) .?.
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