If A=170 degrees,prove that,tan A/2=(-1-root(1+tan^2A))/tanA?

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Answer 1 · 2017-10-24T03:24:31

We know

#tanA=(2tan(A/2))/(1-tan^2(A/2))#

Let #tan(A/2)=x#

So #tanA=(2x)/(1-x^2)#

#=>(tanA)x^2+2x-tanA=0#

So #x=tan(A/2)=(-2-sqrt(2^2-4*tanA*tanA))/(2tanA)#

As #tan(A/2)=tan85^@" is + ve, negative sign neglected"#

So
#x=tan(A/2)=(-2-2sqrt(1-tan^2A))/(2tanA)#

#=>tan(A/2)=(-1-sqrt(1-tan^2A))/(tanA)#