Which of the following is false? (a) sinxe[-1,1] (b) cosxe [-1,1] (c) cosecxe(-1,1) (d) None of these
Answers
All trigonometric functions are basically the trigonometric ratios of any given angle. For example if we take the functions, f(x)=sin x, f(z) = tan z, etc, we are considering these trigonometric ratios as functions. Since they are considered to be functions, they will have some domain and range.
sin2x + cos2 x = 1
From the given identity, the following things can be interpreted:
cos2x = 1- sin2 x
cos x = √(1- sin2x)
Now we know that cosine function is defined for real values therefore the value inside the root is always non-negative. Therefore,
1- sin2x ≥ 0
sin2x ≤ 1
sin x ∈ [-1, 1]
similar to that all options are write hence option (D) is the correct answer none of these.
Given:
Range of Trigonometric expressions:
sin x = [-1, 1]
cos x = [-1, 1]
cosec x = (-1, 1)
To Find: Wrong statement
Calculation:
- Range is the values of y-axis of the plotted graphs for given expression.
- Graph of sine and cosine trigonometric function varies from -1 to +1 on the vertical axis.
- Cosecant is reciprocal of sine function. So, it will never range between -1 to +1.
- Range of cosecant is R - (-1, 1), where R is real number set.