Question

(1+tan alpha)(1+tan 4alpha)=2 then find alpha

Answer 1

Answer:

alpha = pie/4

Step-by-step explanation:

( 1 + tan(x) )( 1 + tan(4x) )= 2

You can simply use your intuition to solve this...

LHS can only and only be equal 2 if one of the two brackets solve to 2 and the other one 1.

so using the trigonometric table only pie/4 gives you the answer.

Answer 2

Step-by-step explanation:

(1+tan alpha) (1+tan 4alpha) =2= (1+tan alpha) (1+tan4alpha) =2(1) = By comparing Lhs and Rhs we get , 1+tan alpha =2, similarly 1+tan 4alpha=1. Now 1+tan alpha =2, i.e tan alpha =2-1=1. hence tan alpha = 1, only possible when theta is π\4. Now, 1+tan4alpha =1, tan4 alpha =1-1=0. hence, tan4alpha =0, Now if we substitute alpha =π\4, it satisfies tan 4alpha =0 , tan 4×π\4 = tan π=0. Hence alpha is π\4=45° is proved for both 1+tan alpha=2 and 1+tan 4alpha =1. Hence proved