Question

Please answer it fast !!!!

Answer 1

Answer:

We have, cosec A = 2

Now, sin A = 

⇒ sin A = 

We know that sin² A + cos² A = 1

⇒ cos² A = 1 - sin² A

⇒ cos A = √(1-sin² A)

⇒ cos A = √{1- }

⇒ cos A = √(1 - )

⇒ cos A = √()

⇒ cos A = 

We know that tan A = 

⇒ tan A = 

⇒ tan A = 

We need to find  + 

Substituting the values of each trigonometric function obtained earlier, we get:

+  =  + 

=  + 

=  + 

= 

= 

=  × 

=  = 8-6= 2

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

$CosecA = \frac{1}{SinA} = 2$

$\small\black\boxed{SinA = \frac{1}{2}}$

$Sin^2A = \frac{1}{4}$

$1-Cos^2A = \frac{1}{4}$

$Cos^2A = \frac{3}{4}$

$\small\black\boxed{CosA= \frac{\sqrt{3} }{2}}$

$TanA = \frac{SinA}{CosA}$

$\small\black\boxed{TanA = \frac{1}{\sqrt{3} } }$

We need to find

$\frac{1}{tanA} + \frac{sinA}{1+cosA}$

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

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

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

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

$= 2$