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Statement 1: If cosalpha,cosbeta,a n dco...

Statement 1: If `cosalpha,cosbeta,a n dcosgamma` are the direction cosines of any line segment, then `cos^2alpha+cos^2beta+cos^2gamma=1.` Statement 2: If cosalpha,cosbeta,a n dcosgamma are the direction cosines of any line segment, then cos2alpha+cos2beta+cos2gamma=1.

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
B
Obviously, Statement 1 is true.
`cos 2alpha + cos 2 beta + cos 2gamma `
`" " = 2cos^(2) alpha -1 = 2cos^(2) beta -1 + 2cos^(2)gamma -1 `
`" " = 2(cos^(2)alpha = cos^(2) beta + cos^(2)gamma) -3 =2 -3 =-1 `
Hence, Statement 2 is true but does not explain Statement 1 as it is resul derived usint the result in the statement.
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