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Question

If cos(α+β)=35 and sin(αβ)=413 then tan2α=?

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Solution

cos(α+β)=3/5,
sin(αβ)=4/13
α+β+αβ=2α
tan(α+β+αβ)=tan2α
tan2α=tan(α+β)+tan(αβ)(1tan(α+β)tan(αβ)
We have cos(α+β)=35
α+β is in I quadrant.
tan(α+β)=43
sin(αβ)=43
tan(αβ)=4153
tan2α=43+41521413×4153=4(153+3)1315316.

1257534_1329284_ans_c7755873db7f444a9d85d77512555431.PNG

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