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యొక్క ప్రధాన విలువ

Answer (Detailed Solution Below)

Option 2 :

Detailed Solution

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వివరణ:

sinθ = x ⇒ θ = sin-1x, θ ∈ [-π/2, π/2]

sin (sin-1 x) =x -π/2 ≤ x ≤ π/2

మనకు,

= sin-1(sin()) ----- ఎందుకంటే ∈ [, ]

కాబట్టి sin-1(sin()) =

Additional Information విలోమ త్రికోణమితీయ ప్రమేయాల ప్రధాన విలువలు:

ప్రమేయం

డొమైన్

ప్రధాన విలువ యొక్క వ్యాప్తి

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)

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