Question

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Q1. ""If sin α . sin β - cos α . cos β = 1 , show that tan α + tan β =0.""

Answer 1

sin α*sin β -cos α*cosβ =1 ⇒cos (α+β)=-1.

1+tg2(α+β)=1/cos2(α+β)=1 ⇒ 1+tg2(α+β)=1 ⇒tg(α+β)=0.

tan (α +β) =(tan α +tan β )/(1- tan α tan β) =0

⇒ tan α +tan β=0

Answer 2

Step-by-step explanation:

Given,

sin α sin β – cos α cos β + 1 = 0

⇒ cos α cos β − sin α sin β = 1

cos(α + β) = 1

Thus, α + β = 0

Taking “tan” on both sides,

tan(α + β) = tan 0

(tan α + tan β)/(1 – tan α tan β) = 0

tan α + tan β = 0

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