Question:
plz explain how is tan(π+π/2)=tan π/12 and how does tan repeats itself after every π and sin,cos repeat after every π
Answer:
1. tan (Π + Π/2) = tan(Π/2)
tan (Π + θ) = tan(Π/2 + Π/2 + θ)
= tan{Π/2 + (Π/2 + θ)}
= - cot(Π/2 + θ) (Since tan(Π/2 + θ) = - cotθ )
= -{- tanθ} (Since cot(Π/2 + θ) = - tanθ)
= tanθ
=> tan (Π + θ) = tanθ
Now put θ = Π/2
So tan (Π + Π/2) = tan(Π/2)
2. sin (Π + θ) = sinθ
sin (Π + θ) = sin(Π/2 + Π/2 + θ)
= sin{Π/2 + (Π/2 + θ)}
= cos(Π/2 + θ) (Since sin(Π/2 + θ) = cosθ )
= - sinθ (Since cos(Π/2 + θ) = - sinθ)
=> sin (Π + θ) = - sinθ
3. cos (Π + θ) = - cosθ
cos (Π + θ) = cos(Π/2 + Π/2 + θ)
= cos{Π/2 + (Π/2 + θ)}
= - sin(Π/2 + θ) (Since cos(Π/2 + θ) = - sinθ )
= - cosθ (Since sin(Π/2 + θ) = cosθ)
=> cos (Π + θ) = - cosθ
In this way sin, cos and tan repeat itself after every Π.
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