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प्रश्न
If cos (α + β) = `4/5` and sin (α - β) = `5/13` where (α + β) and (α - β) are acute, then find tan 2α.
उत्तर
cos (α + β) = `4/5`
sin (α + β) = `3/5`
tan (α + β) = `3/4`
sin (α - β) = `5/13`
cos (α - β) = `12/13`
tan (α - β) = `5/12`
Now tan 2α = tan [(α + β) + (α - β)]
`= (tan (α + β) + (α - β))/(1 - tan (α + β) tan(α - β))`
`[tan (x + y) = (tan x + tan y)/(1 - tan x tan y)]`
`= (3/4 + 5/12)/(1 - (3/4)(5/12))`
`= ((9 + 5)/12)/((48 - 15)/48)`
`= (14/12)/(33/48)`
`= 14/12 xx 48/33`
`= (14 xx 4)/33`
`therefore tan (2alpha) = 56/33`
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