Question #d5791

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Answer 1 · 2017-04-05T07:37:18

# Y=-sqrt2sin(x+pi/4), or#

#Y=sqrt2sin(x+3pi/4).#

#Y=-sinx-cosx=-(sinx+cosx).#

#:. Y=-sqrt2(1/sqrt2sinx+1/sqrt2cosx)#

#=-sqrt2{sinxcos(pi/4)+cosxsin(pi/4)}#

#:. Y=-sqrt2sin(x+pi/4)#.

If, #A# is reqd. to be #+ve,# then, we can rewrite #Y# as,

#Y=sqrt2{(-1/sqrt2)sinx+(-1/sqrt2)cosx},# so that,

#Y=sqrt2{sinxcos(3pi/4)+cosxsin(3pi/4)}, or,#

#Y=sqrt2sin(x+3pi/4).#

Enjoy Maths.!