If cos (α+β) =(3/5), sin(α-β) = (5/13) and 0

Question

If cos (α+β) =(3/5), sin(α-β) = (5/13) and 0 < α, β < (π/4) then tan (2α ) is equal to : (A) (21/16) (B) (63/52) (C) (33/52) (D) (63/16)

Tardigrade Admin · Accepted Answer

0 < α +β < (π/2) and (-π/4) <α - β < (π/4) if cos (α+β ) = (3/5) then tan(α+β) = (4/3) and if sin (α -β)=(5/13) then tan(α-β)= (5/12) (since α -β here lies in the first quadrant) Now tan(2α)= tan (α+β) +(α-β) = ( tan(α+β)+ tan(α-β)/1- tan(α+β). tan(α-β)) = ((4/3) + (5/12)/1- (4)3 . (5)12 = (63/16)

Q. If $cos (α + β) = \frac{3}{5}, sin (α - β) = \frac{5}{13}$ and $0 < α, β < \frac{π}{4}$ then $tan (2 α)$ is equal to :

$\frac{21}{16}$

$\frac{63}{52}$

$\frac{33}{52}$

$\frac{63}{16}$

Q. If cos(α+β)=53​,sin(α−β)=135​ and 0<α,β<4π​ then tan(2α) is equal to :

1621​

5263​

5233​

1663​

Q. If $cos (α + β) = \frac{3}{5}, sin (α - β) = \frac{5}{13}$ and $0 < α, β < \frac{π}{4}$ then $tan (2 α)$ is equal to :

$\frac{21}{16}$

$\frac{63}{52}$

$\frac{33}{52}$

$\frac{63}{16}$