What is the maximum value of sinx.cosx?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
To determine the value of sinx.cosx, first, we have to find the maximum values of sinx and cosx. sin and cos are the trigonometric functions. Trigonometric functions are the extension of trigonometric ratios to any angle in terms of radian measure.
|
Function |
0° |
30° |
45° |
90° |
|
sine |
0 |
½ |
1/√2 |
1 |
|
cos |
1 |
√3/2 |
1/√2 |
0 |
|
tan |
0 |
1/√3 |
1 |
Not Defined |
Table of content
Answer: The maximum value of sinx.cosx is ½. The detailed solution can be seen below.
For any value of x, the maximum value of sinx = 1
Similarly, for any value of x, the maximum value of cosx = 1
According to the formula: sin2x = 2sinx.cosx
then,
By multiplying ½ on both sides of the above equation, we get:
½ (sin2x) = ½ (2sinx.cosx)
½ (sin2x) = 2/2 (sinx.cosx)
½ (sin2x) = (sinx.cosx) {2 in the numerator will cancel out 2 in the denominator)
Now, we know that the maximum value of sinx = 1, hence the maximum value of sin2x will also be = 1.
Applying, this concept in the equation: ½ (sin2x) = (sinx.cosx), we get:
½ (1) = (sinx.cosx)
½ = sinx.cosx
Hence, sinx.cosx = ½ is the final answer.
Summary:
What is the maximum value of sinx.cosx?
½ is the maximum value of sinx.cosx. The detailed solution can be seen in this post above.
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