The least value of cosθsinθ is:
- A2
1
- B0
- C-1
- D−
2
1
Solution & Step-by-step Explanation
Let the expression be E=cosθsinθ.
Multiply and divide by 2:
E=
2
2sinθcosθ
=
2
sin(2θ)
We know that the range of the sine function for any real angle ϕ=2θ is:
−1≤sin(2θ)≤1
To find the least value of E, we substitute the minimum value of sin(2θ), which is −1:
Least Value=
2
−1
=−
2
1
Multiply and divide by 2:
E=
2
2sinθcosθ
=
2
sin(2θ)
We know that the range of the sine function for any real angle ϕ=2θ is:
−1≤sin(2θ)≤1
To find the least value of E, we substitute the minimum value of sin(2θ), which is −1:
Least Value=
2
−1
=−
2
1