Anyone help me here please

 see proof below

Step-by-step explanation:

Use the Double Angle Identity: cos 2A = 2cos²A - 1

Proof  LHS → RHS

Given:                                

LHS:                                   cos 2A

Double Angle Identity:      2(cos²A) - 1

Simplify:                          

Factor:                        

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).