Question

if cos theta = 2 show that cot theta + sin theta / 1 + cos theta = 2

Answer 1

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Answer 2

Answer:

$If \: cosec\theta = 2 \: then\\ cot\theta+\frac{sin\theta}{(1+cos\theta)}=2$

Step-by-step explanation:

$Given \: cosec\theta = 2 --(1)$

$LHS = cot\theta+\frac{sin\theta}{(1+cos\theta)}$

$=cot\theta+\frac{sin\theta(1-cos\theta)}{(1+cos\theta)(1-cos\theta)}$

$=cot\theta+\frac{sin\theta(1-cos\theta)}{1^{2}-cos^{2}\theta}$

$=cot\theta+\frac{sin\theta(1-cos\theta)}{sin^{2}\theta}$

$=cot\theta+\frac{(1-cos\theta)}{sin\theta}$

$=cot\theta+\frac{1}{sin\theta}-\frac{cos\theta}{sin\theta}$

$=cot\theta+cosec\theta-cot\theta$

$=cosec\theta\\=2\:[From\:(1)]\\=RHS$

Therefore,

$If \: cosec\theta = 2 \: then\\ cot\theta+\frac{sin\theta}{(1+cos\theta)}=2$

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