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Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
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Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1...
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Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1...
Evaluation of Trigonometric Expressions
Solution
Step 1: Evaluate sin^2 30 cos^2 45
We know that:
- sin 30 = 1/2
- cos 45 = 1/√2
Substituting these values, we get:
sin^2 30 cos^2 45 = (1/2)^2 (1/√2)^2
= 1/8
Step 2: Evaluate 4tan^2 30
We know that:
- tan 30 = sin 30/cos 30 = (1/2)/(√3/2) = √3/3
Substituting this value, we get:
4tan^2 30 = 4(√3/3)^2
= 4/3
Step 3: Evaluate 1/2 sin^2 90 - 2cos^2 90
We know that:
- sin 90 = 1
- cos 90 = 0
Substituting these values, we get:
1/2 sin^2 90 - 2cos^2 90 = 1/2 (1)^2 - 2(0)^2
= 1/2
Step 4: Evaluate 1/24
We don't need to evaluate this expression as it is already given.
Final Answer
sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24 = 1/8 + 4/3 + 1/2 - 1/2 + 1/24
= 49/24
Therefore, the final answer is 49/24.
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Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?.
Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate. sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?.
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