1.

In `DeltaABC`, a=9,b=8 and c=4, prove that: `cosB-2cosC=-4/3`

Answer» `cosB=(c^(2)+a^(2)-b^(2))/(2ca)=(4^(2)+9^(2)-8^(2))/(2 xx 4 xx 9)`
`=(16+81-64)/(72)=33/72`
and `cosC=(a^(2)+b^(2)-c^(2))/(2ab)`
`=(9^(2)+8^(2)-4^(2))/(2 xx 9 xx 8)`
`=(81 +64-16)/(144)=129/144`
Now `cosB-2cosC=33/72-(2 xx 129)/(144)`
`=33/72-129/72=-96/72=-4/3`.
Hence Proved.


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