(a) if sinθ=21/29, prove that secθ + tanθ=5/2 if θ lies between 0 and Π/2.
(b) what will be the value of the expression when θ lies: (1) between Π/2 and Π. (2) b/w Π and 3Π/2?
please solve this question
If sinθ=21/29 then sec θ = 29/20 and tan θ =21/20 if θ is in I quadrant i.e between 0 and Π/2.
So secθ + tanθ=29/20+21/20 =50/20=5/2
If θ is between Π/2 and Π i.e II Quadrant sec θ = -29/20 and tan θ = - 21/20
secθ + tanθ=-(29/20+21/20) = -50/20= -5/2
If θ is between Π and 3Π/2 i.e III quadrant then tan is positive and sec isnegative i.e tan θ =21/20 and
sec θ = -29/20
Simplify to get secθ + tanθ = -8/20 or -2/5