If cos- -cos- -cos-cos-cos- then prove that tan - -2 -tan - -2 - -2

tan ^ 2 θ #160; 2 #160; = 1 cosθ #160; #160; 1+cosθ #160; #160; =( 1 cosα #160; cosβ #160; #160; 1 cosα #160; cosβ #160; ...

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Basics of Geometry

If cosθ =co...

Question

If $cos θ = \frac{cos α - cos β}{cos α cos β}$ , then prove that
$tan (θ / 2) = \pm tan (α / 2) cot (β / 2)$

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If $c o s θ = \frac{c o s α + c o s β}{1 + c o s α c o s β}$ , prove that $t a n \frac{θ}{2} = \pm t a n \frac{α}{2} t a n \frac{β}{2}$

cos θ = \frac{cos α - cos β}{1 - cos α cos β}

tan \frac{θ}{2}

cos θ = \frac{cos α cos β}{1 - sin α sin β}

tan \frac{θ}{2} = \frac{tan \frac{α}{2} - tan \frac{β}{2}}{1 - tan \frac{α}{2} tan \frac{β}{2}}

{cos}^{- 1} [\frac{cos α + cos β}{1 + cos α cos β}] = 2 {tan}^{- 1} (tan \frac{α}{2} tan \frac{β}{2})

cos θ = \frac{cos α - e}{1 - e cos α}

tan \frac{θ}{2} = \pm \sqrt{\frac{1 + e}{1 - e}} tan \frac{α}{2}

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