AP EAMCET · Maths · Inverse Trigonometric Functions
Consider the following statements.
I. \(\sin ^{-1}\left(y^2-4 y+6\right)+\cos ^{-1}\left(y^2-4 y+6\right) =\frac{\pi}{2}, \forall y \in R\)
II. \(\sec ^{-1}\left(y^2-4 y+6\right)+\operatorname{cosec}^{-1}\left(y^2-4 y+6\right) =\frac{\pi}{2}, \forall y \in R\)
Which of the above statement(s) is/are true?
- A Only I
- B Only II
- C Both I and II
- D Neither I nor II
Answer & Solution
Correct Answer
(B) Only II
Step-by-step Solution
Detailed explanation
Given statements, \(\sin ^{-1}\left(y^2-4 y+6\right)+\cos ^{-1}\left(y^2-4 y+6\right)=\frac{\pi}{2}\) \(\because y^2-4 y+6=(y-2)^2+2 \geq 2, \forall y \in R \text {. }\) So, statement (i) is false and statement (ii) is true.
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