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प्रश्न
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
उत्तर
Let y = `cos^-1 ((sin x + cosx)/sqrt(x))`
= `cos^-1 [1/sqrt(2) sin x + 1/sqrt(2) cos x]`
= `cos^-1 [sin pi/4 sin x + cos pi/4 * cos x]`
= `cos^-1 [cos(pi/4 - x)]`
y = `pi/4 - x` ......`[∵ - pi/4 < x < pi/4]`
Differentiating both sides w.r.t. x
`"dy"/"dx"` = – 1
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