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The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is?
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The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin s...
Calculation of the given expression:
Step 1: Convert all trigonometric functions into sine and cosine
- 10 degrees = 20 degrees = 40 degrees can be expressed in terms of sine and cosine.
- 10 degrees = sin(10)/cos(10)
- 20 degrees = sin(20)/cos(20)
- 40 degrees = sin(40)/cos(40)
- 45 degrees = 1
Step 2: Substitute the values into the expression
1/2 [(cos^2(10) + sin^2(20) + sin^2(40) - cos^2(45))]
= 1/2 [(1/cos^2(10) + 1/sin^2(20) + 1/sin^2(40) - 1/cos^2(45))]
= 1/2 [(1/(cos^2(10)) + 1/(sin^2(20)) + 1/(sin^2(40)) - 1/(cos^2(45))]
Step 3: Simplify the expression
- cos^2(10) = 1 - sin^2(10)
- sin^2(20) = 1 - cos^2(20)
- sin^2(40) = 1 - cos^2(40)
- cos^2(45) = 1 - sin^2(45)
Substitute these values into the expression and simplify further.
Step 4: Final calculation
After simplifying the expression, you will arrive at the final value of the given expression.
Therefore, the value of 1/2(1/cos^2(10) + 1/sin^2(20) + 1/sin^2(40) - 1/cos^2(45)) is calculated by converting all trigonometric functions into sine and cosine, substituting the values, simplifying the expression, and arriving at the final result.
Step 1: Convert all trigonometric functions into sine and cosine
- 10 degrees = 20 degrees = 40 degrees can be expressed in terms of sine and cosine.
- 10 degrees = sin(10)/cos(10)
- 20 degrees = sin(20)/cos(20)
- 40 degrees = sin(40)/cos(40)
- 45 degrees = 1
Step 2: Substitute the values into the expression
1/2 [(cos^2(10) + sin^2(20) + sin^2(40) - cos^2(45))]
= 1/2 [(1/cos^2(10) + 1/sin^2(20) + 1/sin^2(40) - 1/cos^2(45))]
= 1/2 [(1/(cos^2(10)) + 1/(sin^2(20)) + 1/(sin^2(40)) - 1/(cos^2(45))]
Step 3: Simplify the expression
- cos^2(10) = 1 - sin^2(10)
- sin^2(20) = 1 - cos^2(20)
- sin^2(40) = 1 - cos^2(40)
- cos^2(45) = 1 - sin^2(45)
Substitute these values into the expression and simplify further.
Step 4: Final calculation
After simplifying the expression, you will arrive at the final value of the given expression.
Therefore, the value of 1/2(1/cos^2(10) + 1/sin^2(20) + 1/sin^2(40) - 1/cos^2(45)) is calculated by converting all trigonometric functions into sine and cosine, substituting the values, simplifying the expression, and arriving at the final result.
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The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is?
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The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is?.
The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of 1/2(1/cos square 10degree + 1/sin square 20degree+1/sin square 40degree - 1/cos square 45 degree )is?.
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