If $$cos$$⁡$$($$α$$+$$β$$)=4/5$$ and $$sin$$⁡$$($$α−β$$)=5/13$$ where $$0$$≤α,β≤π$$/4$$, then $$tan$$⁡$$2$$α$$=$$

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If $$cos$$⁡$$($$α$$+$$β$$)=4/5$$ and $$sin$$⁡$$($$α−β$$)=5/13$$ where $$0$$≤α,β≤π$$/4$$, then $$tan$$⁡$$2$$α$$=$$

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$$0$$≤α,β≤π$$/4$$⇒ $$0$$≤α$$+$$β≤π$$/2$$ ⇒−π$$/4$$≤α−β≤π$$/4Now$$ $$cos$$⁡$$($$α$$+$$β$$)=4/5$$ ⇒ $$tan$$⁡$$($$α$$+$$β$$)=3/4and$$ $$sin$$⁡$$($$α−β$$)=5/13$$ ⇒ $$tan$$⁡$$($$α−β$$)=5/12we$$ have $$tan$$⁡$$2$$α$$=$$$$tan$$⁡[$$($$α$$+$$β$$)+($$α−β$$)$$]$$=$$$$tan$$⁡$$($$α$$+$$β$$)+$$$$tan$$⁡$$($$α−β$$)1$$−$$tan$$⁡$$($$α$$+$$β$$)$$$$tan$$⁡$$($$α−β$$)=(3/4)+(5/12)1$$−$$(3/4)(5/12)=14/1233/48=5633$$.

If $\cos (α + β) = 4 / 5$ and $\sin (α - β) = 5 / 13$ where $0 \leq α, β \leq π / 4$ , then $\tan 2 α =$

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If cos⁡(α+β)=4/5 and sin⁡(α−β)=5/13 where 0≤α,β≤π/4, then tan⁡2α=

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If $\cos (α + β) = 4 / 5$ and $\sin (α - β) = 5 / 13$ where $0 \leq α, β \leq π / 4$ , then $\tan 2 α =$