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If 2 cosθ + sinθ = 1, then maximum value of 7 cosθ + 6 sinθ is
Correct answer is '6'. Can you explain this answer?
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If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answ...
Explanation:
Given Equation:
2 cos + sin = 1
Step 1: Finding the values of cos and sin
To find the values of cos and sin, we can square both sides of the given equation:
(2 cos + sin)^2 = 1^2
4 cos^2 + 4 cos sin + sin^2 = 1
4 cos^2 + 4 cos sin + 1 - cos^2 = 1
3 cos^2 + 4 cos sin - 1 = 0
Step 2: Solving the Quadratic Equation
Now, we have a quadratic equation in terms of cos and sin. We can solve this equation to find the values of cos and sin.
Step 3: Maximum value of 7 cos + 6 sin
To find the maximum value of 7 cos + 6 sin, we can express it in terms of cos and sin:
7 cos + 6 sin = 7 cos + 6(1 - 2 cos)
= 6 + cos(7 - 12)
= 6 - 5 cos
Since the maximum value of cos is 1, the maximum value of 7 cos + 6 sin = 6 - 5(1) = 6.
Therefore, the maximum value of 7 cos + 6 sin is 6.
Given Equation:
2 cos + sin = 1
Step 1: Finding the values of cos and sin
To find the values of cos and sin, we can square both sides of the given equation:
(2 cos + sin)^2 = 1^2
4 cos^2 + 4 cos sin + sin^2 = 1
4 cos^2 + 4 cos sin + 1 - cos^2 = 1
3 cos^2 + 4 cos sin - 1 = 0
Step 2: Solving the Quadratic Equation
Now, we have a quadratic equation in terms of cos and sin. We can solve this equation to find the values of cos and sin.
Step 3: Maximum value of 7 cos + 6 sin
To find the maximum value of 7 cos + 6 sin, we can express it in terms of cos and sin:
7 cos + 6 sin = 7 cos + 6(1 - 2 cos)
= 6 + cos(7 - 12)
= 6 - 5 cos
Since the maximum value of cos is 1, the maximum value of 7 cos + 6 sin = 6 - 5(1) = 6.
Therefore, the maximum value of 7 cos + 6 sin is 6.
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If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer?
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If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer?.
If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2 cos + sin = 1, then maximum value of 7 cos + 6 sin isCorrect answer is '6'. Can you explain this answer?.
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