B R S are two points on a circle,
Centre O.
TS is a tangent to the circle.
Angle RST = x
Prove that ROS=2X
You must give reasons for each stage
of your working

Proved!

Step-by-step explanation:

Since TS is a tangent to the circle, ∠TSO = 90°.

Hence, ∠OSR = 90° - x.

Since OS and OR are radius, OS = OR.

So, ∠ORS = ∠OSR = 90° - x.

Thus, ∠ROS = 180° - ∠OSR - ∠ORS = 180° - 2 * (90° - x) = 180° - 180° + 2x = 2x.

So, it is proved.

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).