Question

tan thita÷2=tan^3 fi÷2 and tan fi =,2tan alpha prove that fi+theta =2alpha

Answer 1

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Answer 2

GIVEN :

Let A,B,C be substitutes of theta ,fi and alpha respectively.

TanB= 2 tanC

Tan( A/2) = tan^3 (B/2)

TO FIND :

PROVE

(A+B) =2C

SOLUTION :

◆Tan (A/2 + B/2)

= {TanA/2+TanB/2} ÷

{1-TanA/2TanB/2}

={Tan^3 B/2+ TanB/2 } ÷

{1-Tan^3B/2TanB/2}

◆Since,Tan( A/2) = tan^3 (B/2)

=( 1 + Tan^2B/2)Tan( B/2) ÷

( 1 + Tan^2B/2)(1-Tan^2( B/2)

◆a^2 -b^2 =(a-b)( a+ b)

=2Tan( B/2) ×1/2 ÷( 1 - Tan^2B/2)

= TanB ×1/2 = TanC .

◆Since, TanB= 2 tanC

◆Solving,

(A+B )/2 = C

◆A+B =2C

Hence proved.