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Question
Assertion (A): Value of the expression `sin^-1 (sqrt(3)/2) + tan^-1 1 - sec^-1 (sqrt(2))` is `π/4`.
Reason (R): Principal value branch of sin–1 x is `[-π/2, π/2]` and that of sec–1 x is `[0, π] - {π/2}`.
Options
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both (A) and (R) are true but (R) is not the correct explanation of (A).
(A) is true but (R) is false.
(A) is false but (R) is true.
MCQ
Assertion and Reasoning
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Solution
(A) is false but (R) is true.
Explanation:
`sin^-1 (sqrt(3)/2) + tan^-1 1 - sec^-1 (sqrt(2))`
= `π/3 + π/4 - π/4`
= `π/3 ≠ π/4`
So, A is false.
Principal value branch of sin–1 x is `[-π/2, π/2]` and that of sec–1 x is `[0, π] - {π/2}`.
So, R is true.
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