Domain and Range of Basic Inverse Trigonometric Functions
If sin-1 x + ...
Question
If sin−1x+sin−1y+sin−1z=3π2 and f(1)=2,f(a+b)=f(a)f(b) for all a,b,ϵR, then xf(1)+yf(2)+zf(3)−x+y+zxf(1)+yf(2)+zf(3) is equal to :
A
10
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B
11
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C
2
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D
3
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Solution
The correct option is C 2 Since −π2≤sin−1x,sin−1y,sin−1z≤π2 sin−1x+sin−1y+sin−1z=3π2 ⇒sin−1x=sin−1y=sin−1z=π2 ⇒x=y=z=1 ∴xf(1)+yf(2)+zf(3)−x+y+zxf(1)+yf(2)+zf(3) =1+1+1−(1+1+11+1+1)=3−1=2