SOLUTION: Eliminate 0(theta)between the equation q tan 0(theta) + p sec 0(theta)=x p tan 0(theta) + q sec 0(theta)=y

Question 319403: Eliminate 0(theta)between the equation
q tan 0(theta) + p sec 0(theta)=x
p tan 0(theta) + q sec 0(theta)=y
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Eliminate 0(theta)between the equation
q tan(theta) + p sec(theta)=x
p tan(theta) + q sec(theta)=y
------
Rearrange:
q tan(theta) + p sec(theta)=x
q sec(theta) + p tan(theta)=y
--------------
Multiply thru the 1st equation by sec(theta)
Multiply thru the 2nd equation by tan(theta)
---
q(sec)(tan) + p sec^2 = x*sec
q(sec)(tan) + p tan^2 = y*tan
-----------------------------------
Subtract the 2nd equation from the 1st to get:
p(sec^2-tan^2) = x*sec-y*tan
---
Note sec^2-tan^2 = 1
---
p = x*sec-y*tan
----------------------
Substitute for "p" and solve for "q".
========================================
Cheers,
Stan H.
========================================

RELATED QUESTIONS
Find all solutions of the equation tan theta+cot theta+sec theta+csc... (answered by jsmallt9)

Please solve the equation: sec theta- tan theta=0 for... (answered by solver91311)

The equation, with restriction on x, is the terminal side of an angle theta on standard... (answered by stanbon)

Solve the equation on the interval 0< theta < 2pi sec^2theta+tan... (answered by lwsshak3)

Evaluate the expression. tan(90-theta)*tan(theta)*sec(theta) a)1 b)0 c)sec(theta) (answered by KMST)

if tan theta=10/7, and if cos theta <0 then, sec theta= cos theta= sin theta= tan... (answered by Alan3354)

Given tan(theta)=-4/5 and cos(theta)>0, find the exact values of sin(theta) and... (answered by stanbon)

Given tan theta=-4/5 and cos theta > 0, find the exact values of sin theta and sec... (answered by Alan3354)

solve the equation cos theta - tan theta * cos theta = 0 for 0< theta < 2... (answered by stanbon,DrBeeee)