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The minimum value of cos2x+cosx is?
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The minimum value of cos2x+cosx is?
Minimum value of cos2x + cosx
The expression cos2x + cosx can be simplified using trigonometric identities to find its minimum value.
Using Double Angle Identity
cos2x = 2cos^2x - 1
Substitute the Double Angle Identity
cos2x + cosx = 2cos^2x - 1 + cosx
Rearrange the terms
cos2x + cosx = 2cos^2x + cosx - 1
Using Quadratic Equation
To find the minimum value, consider the expression as a quadratic equation in terms of cosx: 2cos^2x + cosx - 1
Find the minimum value
The minimum value of a quadratic equation ax^2 + bx + c is given by -b/2a. Therefore, the minimum value of 2cos^2x + cosx - 1 is -1/(2*2) = -1/4.
Therefore, the minimum value of cos2x + cosx is -1/4.
The expression cos2x + cosx can be simplified using trigonometric identities to find its minimum value.
Using Double Angle Identity
cos2x = 2cos^2x - 1
Substitute the Double Angle Identity
cos2x + cosx = 2cos^2x - 1 + cosx
Rearrange the terms
cos2x + cosx = 2cos^2x + cosx - 1
Using Quadratic Equation
To find the minimum value, consider the expression as a quadratic equation in terms of cosx: 2cos^2x + cosx - 1
Find the minimum value
The minimum value of a quadratic equation ax^2 + bx + c is given by -b/2a. Therefore, the minimum value of 2cos^2x + cosx - 1 is -1/(2*2) = -1/4.
Therefore, the minimum value of cos2x + cosx is -1/4.
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The minimum value of cos2x+cosx is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The minimum value of cos2x+cosx is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum value of cos2x+cosx is?.
The minimum value of cos2x+cosx is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The minimum value of cos2x+cosx is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum value of cos2x+cosx is?.
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