Question
Download Solution PDFFind the principal value of
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
| Function | Domain | Range of Principal Value |
| sin-1 x | [-1, 1] | [-π/2, π/2] |
| cos-1 x | [-1, 1] | [0, π] |
| csc-1 x | R - (-1, 1) | [-π/2, π/2] - {0} |
| sec-1 x | R - (-1, 1) | [0, π] - {π/2} |
| tan-1 x | R | (-π/2, π/2) |
| cot-1 x | R | (0, π) |
| sin-1 (-x) | - sin-1 x | cos-1 (-x) | π - cos-1 x |
| cosec-1 (-x) | - cosec-1 x | sec-1 (-x) | π - sec-1 x |
| tan-1 (-x) | - tan-1 x | cot-1 (-x) | π - cot-1 x |
Calculation:
As we know sin-1 (-x) = - sin-1 x
So,
Let
⇒ sin θ =
∴ θ = 45°
Hence,
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