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If x , y , z are in A.P., then (sinx-sin...

If `x , y , z` are in A.P., then `(sinx-sinz)/(cosz-cosx)` is equal to

A

`tany`

B

`coty`

C

`siny`

D

`cosy`

Text Solution

Verified by Experts

As `x,y and z` are in A.P.
`:. 2y = z+x`
`=>y = (z+x)/2`
Now, `(sinx-sinz)/(cosz-cosx) = (2sin((x-z)/2)cos((x+z)/2))/(2sin((x-z)/2)sin((z+x)/2))`
`= cosy/siny = cot y`
`:. (sinx-sinz)/(cosz-cosx) = coty`
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