UPSC Exam > UPSC Questions > Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)?
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Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)?
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Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)?
Expression Evaluation
Given Expression: 4(sin⁴30+cos⁴60)-3(cos²45-sin²90)
Step 1: Evaluate each trigonometric function at given angles
- sin 30° = 0.5
- cos 60° = 0.5
- cos 45° = sin 45° = 1/√2
- sin 90° = 1
Step 2: Substitute the values into the expression
- sin⁴30 = (0.5)⁴ = 0.0625
- cos⁴60 = (0.5)⁴ = 0.0625
- cos²45 = sin²45 = (1/√2)² = 1/2
- sin²90 = 1² = 1
Step 3: Simplify the expression
= 4(0.0625 + 0.0625) - 3(1/2 - 1)
= 4(0.125) - 3(1/2 - 1)
= 0.5 - 3(-0.5)
= 0.5 + 1.5
= 2
Final Answer: The value of the given expression is 2.
Expression Evaluation
Given Expression: 4(sin⁴30+cos⁴60)-3(cos²45-sin²90)
Step 1: Evaluate each trigonometric function at given angles
- sin 30° = 0.5
- cos 60° = 0.5
- cos 45° = sin 45° = 1/√2
- sin 90° = 1
Step 2: Substitute the values into the expression
- sin⁴30 = (0.5)⁴ = 0.0625
- cos⁴60 = (0.5)⁴ = 0.0625
- cos²45 = sin²45 = (1/√2)² = 1/2
- sin²90 = 1² = 1
Step 3: Simplify the expression
= 4(0.0625 + 0.0625) - 3(1/2 - 1)
= 4(0.125) - 3(1/2 - 1)
= 0.5 - 3(-0.5)
= 0.5 + 1.5
= 2
Final Answer: The value of the given expression is 2.
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Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)?
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Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)?.
Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate:4(sin⁴30+cos⁴60)-3(cos²45-sin²90)?.
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