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a line makes an angle X,Y,Z with the coordinate axes.if X+Y=90 then [cosX+cosY+cosZ]^2 is

a line  makes an angle X,Y,Z with the coordinate axes.if X+Y=90 then [cosX+cosY+cosZ]^2 is

Grade:12

1 Answers

prince sunjot dutt
58 Points
2 years ago
We know that:
cos²x+cos²y+cos²z=1
Given_ x+y=90
=cos²x+cos²(90-x)+cos²z=1
=cos²x+sin²x+cos²z=1
=1+cos²z=1
=cos²z=0
=z=π/2
Now,
(cosx+cosy+cosz)²
(Cosx+cos(90-x)+cosπ/2)²
(Cosx+siny)²
Cos²x+sin²y+2cosxsiny
1+ 2cos(90-y)siny
1+2sinycosy
1+sin2y
 

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