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costheta=(a^(2)+b^(2))/(2ab), where a an...

`costheta=(a^(2)+b^(2))/(2ab)`, where a and b are two distinct numbers such that `ab gt 0`.

Text Solution

Verified by Experts

False,
Given, a is a positive number and `a ne 1`, then AM `gt` GM
(since, AM and GM of two number's a and b are `(a+b)/2` and `sqrt(ab)`, respectively]
`rArr (a^(2)+b^(2))/(2) gt sqrt(a^(2).b^(2))`
`rArr a^(2) + b^(2) gt 2ab`
`rArr (a^(2) + b^(2))/(2ab) gt 1` `[therefore cos theta=(a^(2)+b^(2))/(2ab)]`
`rArr costhetagt1` `[therefore -1 lecos theta le1]`
Which is not possible
Hence, `costheta ne (a^(2) + b^(2))/(2ab)`
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