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Let g(x)= ax + b , where a lt 0 and g...

Let `g(x)= ax + b ` , where ` a lt 0 ` and g is defined from [1,3] onto [0,2] then the value of ` cot ( cos^(-1) (|sin x | + |cos x|) + sin^(-1)(-|cos x | - |sinx|)) ` is equal to :

A

`g(1)`

B

`g(2)`

C

`g(3)`

D

`g(1)+g(3)`

Text Solution

Verified by Experts

Let g(x)=ax+b, where `a lt 0` and g is defined from [1,3] onto [0,2] then the value of
`cot(cos^(-1)(|sinx|+|cos x|)+sin^(-1)(-|cosx|-|sinx|))` is equal to
(A) g (B) g(2) (C*)g(3) (D)g(1)+g(3)
Consider `F(s)=cot(cos^(-1)(|sinx|+|cos x|)+sin^(-1)(-|cosx|-|sinx|))`
But `|sinx|+|cosx| in [1,sqrt(2)]AA x in R`
`:. F(x)=cot(cos^(-1)(1)+sin^(-1)(-1))=cot(0-(pi)/(2))=0=g(3)" " `(AsF(x)=0,`AAx in D_(F)`)
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