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Simplify : sin^-1 [sinx+cosx/square root 2], -pi/4

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Solution: We have ,

$sin^-1[sin x+cos x/sqrt2]$

$Rightarrow$ $sin^-1[1/sqrt2 cdot sin x + 1/sqrt2cdot cos x]$

$Rightarrow$ $sin^-1[sin xcdot cos pi/4 +cos xcdot sin pi/4]$

$Rightarrow$ $sin^-1[sin (x+pi/4)]=x+pi/4$

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Deependra Verma

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