Question

what is tanx=2cscx in the interval of -pi 13 years ago

Answer 1

can u explain ur question in detail...are u asking for the value of tanx or x??

Answer 2

here we can write tan x =sin x/cos x
and csc x= 1/sin x
then our equation will be
sin x/cos x = 2/sin x
=>(sin x)^2 =2cos x
=>1-(cos x)^2 =2cos x {as u know (sin x)^2 + (cos x)^2 =1}
=>(cos x)^2+ 2cos x-1=0
=> t^2 +2t -1 =0 (let cos x=t)

now we can find the soln of quadratic eqn

t= {-2+ sqrt(4+4) }/2 or {-2- sqrt(4+4) }/2
= 0.414 or -2.414


but as we know the value of cos x cant be less than -1 ,the 2nd value(-2.414) is discarded...
so we only have
t= 0.414
=> cos x = 0.414
=> x = arc cos (0.414)
=> x = 1.144

so ans is d.