Q. Trig (1 Viewer)

[marsenal]

If tan@=ktanb, show that
(k-1)sin(@+b)=(k+1)sin(@-b)

All I can come up with is getting expressions for sinb, sin@, cosb, cos@ and then expanding both sides of the expression and subbing in those values, but that just seems to be a long and roundabout way of doing this. There must be better ways.

Thanks

 

[bobo123]

well im a newbie so i did it the stupid way so yeah, muscle over brains


if tan a = ktan b
=> sin a cos b = k(sin b cos a)

expanding the sin thing gives

=> (k-1)(sin a cos b )+(k-1)(sin b cos a ) = (k+1)(sin a cos b )-(k+1)(sin b cos a )
=> (k-1-k-1)(sin a cos b ) = (-k-1-k+1)(sin b cos a )
=> -2(sin a cos b ) = -2k(sin b cos a )
=> sin a cos b = k(sin b cos a)

proven?

 

[inasero]

yes thats correctexcept it wouldbe more technically correct if you dont assume the thing youre trying to prove to start off with...thats to say, write the whole thing backwards and bobs your uncle