(1+cosx)/sinx=cot(x/2): I just need help with the first two lines.

[jonokonko]

I just need help with the first two lines.

(1+cosx)/sinx=cot(x/2)

 

[Deleted member 4993]

I just need help with the first two lines.

(1+cosx)/sinx=cot(x/2)

Help with what? What were you asked to calculate?
What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[Ishuda]

I just need help with the first two lines.

(1+cosx)/sinx=cot(x/2)

Several ways to go about showing that the equation is true. Possibly the easiest is to let
u = x/2
and use the double angle formulas for the sine and cosine plus the sin²+cos²=1 identity.

 

[hoosie]

Using Trig double angle formulas

Example:


Show that: sin(6θ)/[1+cos(6θ)] = tan(3θ)


Use double angle formulas:
cos(2θ) = 2cos²θ - 1
sin(2θ) = 2sinθcosθ



Replacing 2θ with 6θ:
cos(6θ) = 2cos²(3θ) - 1
sin(6θ)= 2sin(3θ)cos(3θ)



LHS
= sin(6θ)/[1+cos(6θ)]
= 2sin(3θ)cos(3θ) / [1 + 2cos²(3θ) - 1]
= 2sin(3θ)cos(3θ) / 2cos²(3θ)
= sin(3θ)/cos(3θ)
= tan(3θ)
= RHS