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What is the value of tan 30° sec 45°+ tan 60° sec 30° ?
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What is the value of tan 30° sec 45°+ tan 60° sec 30° ?
Understanding the Components
To solve the expression tan 30° sec 45° + tan 60° sec 30°, we need to evaluate each trigonometric function involved first.
Step 1: Calculate tan 30°
- tan 30° = 1/√3
Step 2: Calculate sec 45°
- sec 45° = 1/cos 45° = 1/(√2/2) = √2
Step 3: Calculate tan 60°
- tan 60° = √3
Step 4: Calculate sec 30°
- sec 30° = 1/cos 30° = 1/(√3/2) = 2/√3
Step 5: Plugging in Values
Now we can substitute the calculated values into the original expression:
- tan 30° sec 45° = (1/√3) * √2 = √2/√3
- tan 60° sec 30° = √3 * (2/√3) = 2
Step 6: Combining the Results
Now, we combine the two results:
- Expression = √2/√3 + 2
Final Calculation
To find a common denominator for the sum:
- Rewrite 2 as (2√3/√3)
- Therefore, the expression becomes: (√2 + 2√3)/√3
Conclusion
The final value of the expression tan 30° sec 45° + tan 60° sec 30° is:
- (√2 + 2√3)/√3
This concludes the evaluation of the given trigonometric expression!
To solve the expression tan 30° sec 45° + tan 60° sec 30°, we need to evaluate each trigonometric function involved first.
Step 1: Calculate tan 30°
- tan 30° = 1/√3
Step 2: Calculate sec 45°
- sec 45° = 1/cos 45° = 1/(√2/2) = √2
Step 3: Calculate tan 60°
- tan 60° = √3
Step 4: Calculate sec 30°
- sec 30° = 1/cos 30° = 1/(√3/2) = 2/√3
Step 5: Plugging in Values
Now we can substitute the calculated values into the original expression:
- tan 30° sec 45° = (1/√3) * √2 = √2/√3
- tan 60° sec 30° = √3 * (2/√3) = 2
Step 6: Combining the Results
Now, we combine the two results:
- Expression = √2/√3 + 2
Final Calculation
To find a common denominator for the sum:
- Rewrite 2 as (2√3/√3)
- Therefore, the expression becomes: (√2 + 2√3)/√3
Conclusion
The final value of the expression tan 30° sec 45° + tan 60° sec 30° is:
- (√2 + 2√3)/√3
This concludes the evaluation of the given trigonometric expression!
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What is the value of tan 30° sec 45°+ tan 60° sec 30° ?
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What is the value of tan 30° sec 45°+ tan 60° sec 30° ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the value of tan 30° sec 45°+ tan 60° sec 30° ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of tan 30° sec 45°+ tan 60° sec 30° ?.
What is the value of tan 30° sec 45°+ tan 60° sec 30° ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the value of tan 30° sec 45°+ tan 60° sec 30° ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of tan 30° sec 45°+ tan 60° sec 30° ?.
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