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Express sin^(-1)((sin x+ cos x)/(sqrt2))...

Express `sin^(-1)((sin x+ cos x)/(sqrt2))`, where `-(pi)/(4) lt x lt (pi)/(4)`, in the simplest form.

Text Solution

Verified by Experts

`=sin^(-1)((sinx)/(sqrt(2))+(cosx)/(sqrt(2)))`if `(pi)/(4)lt xlt (pi)/(4)`
`=sin^(-1)(sinxcos.(pi)/(4)+cosxsin.(pi)/(4))` if `-(pi)/(4)+(pi)/(4)ltx+(pi)/(4)lt(pi)/(4)+(pi)/(4)`
`=sin^(-1)(sin(x+(pi)/(4)))` if `0lt(x+(pi)/(4))lt(pi)/(2)`i.e. principal values
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  • If tan x= (3)/(4) " where " pi lt x lt (3pi)/( 2), value of tan ""(x)/(2) is

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