Question

if Cosec Q = 2,
, show that (cot Q+ sin Q / 1+cos Q) = 2
​

Answer 1

Answer:

cosec Q = 2 = h/p

h² = p² + b²

2² = 1² + b²

4 - 1 = b²

3 = b²

√3 = b

cot Q = b/p = √3/1 = √3

sin Q = p/h = 1/2

cos Q = b/h = √3/2

$cot \: Q + \frac{ sin \: Q}{1 + cos \: Q}$

$\sqrt{3} + \frac{ \frac{1}{2} }{1 + \frac{ \sqrt{3} }{2} }$

$\sqrt{3} + \frac{1}{2 + \sqrt{3} }$

$\frac{2 \sqrt{3} + 3 + 1}{2 + \sqrt{3} }$

$\frac{2 (\sqrt{3} + 2)}{2 + \sqrt{3} }$

$2$

Hope you got your answer

Have a great day ahead