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…

Question

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?

Aicharya · Accepted Answer

Given statements, $\sin ^{-1}\left(y^2-4 y+6ight)+\cos ^{-1}\left(y^2-4 y+6ight)=\frac{\pi}{2}$ $\because y^2-4 y+6=(y-2)^2+2 \geq 2, \forall y \in R 	ext {. }$ So, statement (i) is false and statement (ii) is true.

Consider the following statements. I. $\sin ^{-1}\left(y^2-4 y+6\right)+\cos ^{-1}\left(y^2-4 y+6\right)…

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