I have the following type of equation which I wish

Sahar Bowden

Sahar Bowden

Answered question

2022-02-28

I have the following type of equation which I wish to solve for t:
xcostysint=z

Answer & Explanation

Julien Manning

Julien Manning

Beginner2022-03-01Added 7 answers

xsec(t)ycsc(t)=z
sec(t)=1+T2 and csc(t)=1+T2T where T=tan(t). Therefore
xT1+T2+y1+T2=z
1+T2+y1+T2=z
1+T2=z2x2T2+y2+2xyT
x2T4+2xyT3+(x2+y2)T2+2xyT+y2z2=0
Now I am afraid you will have to solve the equation keeping in mind that the expression zxT+y is positive.

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