(A) |tanx|=mn⇒tanx=mn & tanx=−mn
In [0,2π]it has 4 solutions
(B) cosx+cos2x+cos3x+cos4x+cos5x=5
⇒cosx=cos2x=cos3x=cos4x=cos5x=1
⇒x=2n1π,x=n2π,
x=2n3π3,x=n4π2,x=2n5π5
⇒x=0,2π are common solutions.
(C) 121−|cosx|=4
⇒11−|cosx|=2⇒1−|cosx|=12
⇒|cosx|=12⇒cosx=±12
∴ In (−π,π) there are 4 solutions
(D) tanθ+tan2θ+tan3θ=tanθtan2θtan3θ
⇒θ+2θ+3θ=nπ⇒θ=nπ/6
⇒θ=π3,2π3 satisfy equation only.