यदि `sin x = 1/sqrt(5), sin y=(1)/sqrt(10)`, जहाँ `0 lt x lt pi/2, 0 lt y lt pi/2` है, तो `(x+y)` किसके बराबर है ?

Options

A. `pi`
B. `pi/2`
C. `pi/4`
D. 0

Answer

C

Explanation

हम पाते हैं,
`sinx=1/sqrt(5)` तथा `sin y = 1/sqrt(10)`
`rArr x = sin^(1)((1)/(sqrt(5)))` तथा `y=sin^(-1)(1/sqrt(10))`
अब, `x+y=sin^(-1)(1/sqrt(5))+sin^(-1)(1/sqrt(10))`
`=sin^(-1)[1/sqrt(5)sqrt(r-(1/sqrt(10))^(2))+1/sqrt(10)sqrt(1-(1/sqrt(5))^(2))]` `[:'sin^(-1)x+sin^(-1)y-sin^(-1) (x sqrt(1-y^(2))+ysqrt(1-x^(2)))]`
`=sin^(1)[1/sqrt(5)sqrt(1-1/10)+1/sqrt(10)sqrt(1-1/5)]`
`=sin^(-1)[1/sqrt(5)xx 3/sqrt(10)+1/sqrt(10).2/sqrt(5)]`
`sin^(-1)[(sqrt(5))/(sqrt(5)sqrt(10))]`
`=sin^(-1)(1/sqrt(2))`
`=pi//4 " " [:'sin.(pi)/(4)=1/sqrt(2)]`