Question

If 1+ cos(y-z)tcos(z-x)+cos (x-y)=o then Prove that y-z or z-x is the Odd multiple of pie​

Answer 1

Answer:

cos

−1

x+cos

−1

y+cos

−1

z=π

cos

−1

x+cos

−1

y=π−cos

−1

z

cos

−1

(xy−

1−x

2

1−y

2

)=π−cos

−1

z

xy−

1−x

2

1−y

2

=cos(π−cos

−1

z)

xy−

1−x

2

1−y

2

=−cos(cos

−1

z)

xy−

1−x

2

1−y

2

=−z

xy+z=

1−x

2

1−y

2

(xy+z)

2

=(1−x

2

)(1−y

2

)

x

2

y

2

+z

2

+2xyz=1−x

2

−y

2

+x

2

y

2

x

2

+y

2

+z

2

+2xyz=1