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Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230?
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Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230?
Expression Evaluation:
1. Given Expression:
2cosec^2 30 + 3sin^2 60 - 3/4 tan^2 30
2. Trigonometric Values:
- Cosec 30 = 2
- Sin 60 = √3/2
- Tan 30 = 1/√3
3. Substitute Values:
- Cosec^2 30 = 2^2 = 4
- Sin^2 60 = (√3/2)^2 = 3/4
- Tan^2 30 = (1/√3)^2 = 1/3
4. Expression with Substituted Values:
2(4) + 3(3/4) - 3/4(1/3)
8 + 9/4 - 1/4
32/4 + 9/4 - 1/4
40/4
10
5. Final Evaluation:
The value of the expression 2cosec^2 30 + 3sin^2 60 - 3/4 tan^2 30 is 10.
By substituting the given trigonometric values and simplifying the expression step by step, we arrive at the final result of 10. This process involves basic trigonometric calculations and arithmetic operations to evaluate the given expression accurately.
1. Given Expression:
2cosec^2 30 + 3sin^2 60 - 3/4 tan^2 30
2. Trigonometric Values:
- Cosec 30 = 2
- Sin 60 = √3/2
- Tan 30 = 1/√3
3. Substitute Values:
- Cosec^2 30 = 2^2 = 4
- Sin^2 60 = (√3/2)^2 = 3/4
- Tan^2 30 = (1/√3)^2 = 1/3
4. Expression with Substituted Values:
2(4) + 3(3/4) - 3/4(1/3)
8 + 9/4 - 1/4
32/4 + 9/4 - 1/4
40/4
10
5. Final Evaluation:
The value of the expression 2cosec^2 30 + 3sin^2 60 - 3/4 tan^2 30 is 10.
By substituting the given trigonometric values and simplifying the expression step by step, we arrive at the final result of 10. This process involves basic trigonometric calculations and arithmetic operations to evaluate the given expression accurately.
Community Answer
Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230?
10 2(2)^2+3(√3/2)^2-3/4(1/√3)8+9/4-3/12192+54-6/24246-6/24240/2410
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Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230?
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Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230? 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 Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230?.
Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230? 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 Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate: 2cosec^2 30+3sin^2 60 - 3/4 tan^230?.
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