Maths-
General
Easy
Question
Statement - I For any real value of or
the value of the expression
0 or y≥2 (either less than or equal to zero or greater than or equal to two)
Statement - II for all real values of
.
- Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
- Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I.
- Statement-I is true, Statement-II is false
- Statement-I is false, Statement-II is true
Hint:
In this question, given two statement. It is like assertion and reason. Statement1 is assertion and statement 2 is reason, Find the statement 1 is correct or not and the statement 2 correct or not if correct then is its correct explanation.
The correct answer is: Statement-I is false, Statement-II is true
Here we have to find the which statement is correct and if its correct explanation or not.
Firstly,
Statement-1: For any real value θ ≠ (2n + 1) π or (2n + 1)
, nϵ I, the value of expression
y =( cos^2 θ -1)/ ( cos^2 θ + cos θ) is y ≤ 0 or y ≥ 2 ( either less than or equal to zero or greater than to two.
We have,
![y equals c o s squared theta minus 1 divided by divided by c o s squared theta plus c o s theta](data:image/png;base64,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)
![equals negative s i n squared theta divided by c o s theta left parenthesis c o s theta plus 1 right parenthesis left square bracket s i n squared theta plus c o s squared theta equals 1 right square bracket](data:image/png;base64,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)
![equals negative s i n squared theta divided by 2 c o s theta. C o s squared theta divided by 2
equals left parenthesis 4 s i n squared theta divided by 2. c o s squared theta divided by 2 right parenthesis divided by left parenthesis 2 c o s theta. C o s squared theta divided by 2 right parenthesis
equals negative left parenthesis 2 s i n squared theta divided by 2 right parenthesis divided by c o s theta equals left parenthesis 1 minus c o s theta right parenthesis divided by c o s
equals negative left square bracket s e c theta minus 1 right square bracket
equals 1 minus s e c theta.](data:image/png;base64,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)
Or
![y equals 1 minus s e c theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAAPCAYAAACP3GNFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAgpJREFUeNrtl09ERFEUxp8kI2MYIyNpM4uMZDYZI0mbtEieRFokSbTMLCJJWkVatGibJEkkrZI2STLSJhlJYhYtWrUZs0jGo77LN1x3zsyYMv+e+fiZ986998x959537nmWVRv1gHXwZLlHg+AcfIBbEKv1hI7AIvhxSYBjDHAL7ztAql4m55Ygqzeyy7BdgYhu2AfTwuA42GzwIK+Bd+Dw/1aM9iA4A9/sNyz48IJtpoIsd62fbSPgQBhzAsZ0wxyd6GoHbyBQIDilqIcgqwDvgbYC7T6QBDbve8GzEOBHbjYffS2DcbYr/5OCb7UQo7pBRfzU6LTBw6mR00WCO62Q1MZaNWwXxqJsgd0iPl6KbLSg3jFgrGAucXvqIMj/eWumuAttoU0dUmk+q27LaAeY+v3UUoPkI1OG3frSrneYjyvx4NXOyZ3gDtzw1dcrAmneCa1PlGMLSe3Ua8EeZZ7Pk3IWIiltNd1QXXiYe2c1my2kSFNjzK2lSjdLSLXz0oBD/vGxMRm3lHCqgprR7gfAQ4kx/eC1SLtX+KDyM0WJh22cE0m6sE6O8oAKCIdWnG+tn4fgkFADq8qildVFnF93OamzbInXYXCvVR55muBD21UK7l9yeDlK06/DfBwW+oSYJh0GfEHo083PZIcb0OwT4UJkjXJQlM1VaKqCumSeaqpC6mMR3lQF9AsIqZN88YxPrAAAAJx0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+eTwvbWk+PG1vPj08L21vPjxtbj4xPC9tbj48bW8+JiN4MjIxMjs8L21vPjxtaT5zPC9taT48bWk+ZTwvbWk+PG1pPmM8L21pPjxtaT4mI3gzQjg7PC9taT48L21hdGg+z9qVZAAAAABJRU5ErkJggg==)
![s e c theta equals 1 minus y](data:image/png;base64,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)
As the range of secx is ≤−1 and ≥1
Or
1−y<−1 and 1−y>1
Or
y>2 and y<0.
So statement I is False,
Statement-II – secθ∈(−∞,−1]∪[1,∞) for all real values of θ.
So we know that for all , range of sec x ≤−1 and ≥1,
So secθ∈(−∞,−1]∪[1,∞) for all real values of θ.
Therefore, statement-II is correct.
The correct answer is Statement – I is false, Statement – II is true.
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason
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