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.

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To express \( \sin^{-1}\left(\frac{\sin x + \cos x}{\sqrt{2}}\right) \) in its simplest form, we will follow these steps: ### Step 1: Rewrite the expression We start with the expression: \[ y = \sin^{-1}\left(\frac{\sin x + \cos x}{\sqrt{2}}\right) \] ...

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If cos x + sin x = a (- (pi)/(2) lt x lt - (pi)/(4)) , then cos 2 x is equal to

`a^(2)`

`a sqrt((2-a))`

`a sqrt((2+a))`

`asqrt((2-a^(2)))`

If sec x =- (13)/(12) and (pi)/(2) lt x lt pi , find the value of sin 2x

`(60)/(169)`

`(-60)/(169)`

`(120)/(169)`

`(-120)/(169)`

If int_(0)^(t) (bx cos 4x- a sin 4x)/(x^(2)) dx= (a sin 4t)/(t)-1 , where 0 lt t lt (pi)/(4) , then the value of a, b are equal to

`(1)/(4), 1`

`-1, 4`

2, 2

2, 4