Question

Tan(x+100)=tan(x+50)tanx tan(x-50)

Answer 1

Answer:

Given -:tan(x+1000)=tan(x+500)⋅tan(x)⋅tan(x−500)

⇒tan(x+1000)tan(x−500)⇒=tan(x+500)⋅tan(x0)

⇒sin(x+1000)⋅cos(x−500)cos(x+1000)⋅sin(x−500)=sin(x+500)⋅sin(x)cos(x+500)⋅cos(x)

Using Componendo and dividendo,

⇒sin(2x+500)sin(1500)=−cos(500)cos(2x+500)

⇒sin(4x+1000)=−cos(500)=−sin(500)=sin(1800+400)=sin(3600−400)

⇒(4x+1000)=2200=3200

So x=300 or x=550