Question

if cosec = 2 , show that (cot + sin/1 + cos) = 2
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Answer 1

Answer:

Given :-

Cosec a=2

To prove :-

$\frac{cot \: a + sin \: a}{1 + cos \: a} = \: 2$

Proof :-

Trigonometry is the branch of mathematics that deals with right angled triangles.

There is hypotenuse(h), perpendicular (p) and base (b).

Sin a = p/h

Cos a = b/h

Tan a = p/b

Cot a = b/p

Sec a = h/b

Cosec a = h/p

And,

As Cosec =hypotenuse /perpendicular

Cosec = h/p=2

Then, using Pythagoras theorem,

p²+b²=h²

1²+b²=2²

b²=2²-1²=4-1=3

b=√3

$Now \: ,as \: sin a = \frac{1}{cosec \: a} = \frac{1}{2} \\ cos \: a = \frac{b}{h} = \frac{ \sqrt{3} }{2} \\ cot \: a = \frac{b}{p} = \frac{ \sqrt{3} }{1}$

Now putting these values in the equation, we get

$= > \frac{cot \: a + sin \: a}{1 + cos \: a}$

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

$= > 2$

Hence proved.

Answer 2

Step-by-step explanation:

$\large{\boxed{\sf{\red{hope \: this \: will \: help \: you}}}} >$