1.

If `alpha` and `beta` are acute angles and `cot alpha=1/4` and `cot beta=5/3`. prove that `alpha-beta=45`

Answer» `cotalpha=1/4,tanalpha=4`
`cotbeta=5/,tanbeta=3/5`
`tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)`
`=(4-3/5)/(1+12/5)=1`
`alpha-beta=45^o`
since `alpha<90^o`
`beta<90^o`.


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