Prove that- tan-tan-sin 2-1-sin2 -sin2-

Now, tan(α+β)+tan(α β) =sin (α+ β)cos(α+β)+sin (α β)cos (α β) =sin(α+β).cos(α β) sin(α β).cos(α+β)cos (α+β).cos (α β) =sin(α+β+α β)cos^2 α si ...

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Trigonometric Ratios of Compound Angles

Prove that: ...

Question

Prove that:
$tan (α + β) + tan (α - β) = \frac{sin 2 α}{1 - {sin}^{2} α - {sin}^{2} β}$

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β = \frac{tan α + tan γ}{1 + tan α tan γ},

sin 2 β = \frac{sin 2 α + sin 2 γ}{1 + sin 2 α sin 2 γ}

\frac{t a n (α + β - γ)}{t a n (α - β + γ)} = \frac{t a n γ}{t a n β}

s i n (β - γ) = 0

s i n 2 α + s i n 2 β + s i n 2 γ = 0

tan β = \frac{tan α + tan γ}{1 + tan α tan γ}

sin 2 β = \frac{sin 2 α + sin 2 γ}{1 + sin 2 α sin 2 γ} .

sin 2 α = 4 sin 2 β

\frac{5 tan (α - β)}{tan (α + β)} =

0 \leq α, β \leq 90

tan (α + β) = 3

tan (α - β) = 2

sin 2 α

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