IF x cos(alpha)+ ysin( alpha)=1, a b x cos(Beta) + y sin(Beta)=1 and a b cos(alpha)cos(Beta) + a 2 sin(alpha)sin(Beta) =0 then b 2 prove that: tan(alpha)tan(beta)={b 2 (x 2 - a 2 )}/{a 2 (y 2 - b 2 )}

Question

Ravi · Answer

Subtract the forst 2 eqns to obtain :
i) a relation between alpha and beta
ii) A trigonometric eqn with alpha and beta in terms of x,y,a,b

Use these 2 conditions to form a simpler eqn. Use the obtained equality in the third eqn to get to the desired answer.

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IF x cos(alpha)+ ysin( alpha)=1, a b x cos(Beta) + y sin(Beta)=1 and a b cos(alpha)cos(Beta) + a 2 sin(alpha)sin(Beta) =0 then b 2 prove that: tan(alpha)tan(beta)={b 2 (x 2 - a 2 )}/{a 2 (y 2 - b 2 )}

IF x cos(alpha)+ ysin(alpha)=1,
a b
xcos(Beta) + ysin(Beta)=1 and
a b
cos(alpha)cos(Beta)  +
   a²
sin(alpha)sin(Beta) =0 then
   b²
prove that:
tan(alpha)tan(beta)={b²(x²- a²)}/{a²(y²- b²)}

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IF x cos(alpha)+ ysin( alpha)=1, a b x cos(Beta) + y sin(Beta)=1 and a b cos(alpha)cos(Beta) + a 2 sin(alpha)sin(Beta) =0 then b 2 prove that: tan(alpha)tan(beta)={b 2 (x 2 - a 2 )}/{a 2 (y 2 - b 2 )}

IF x cos(alpha)+ ysin(alpha)=1, a bxcos(Beta) + ysin(Beta)=1 anda bcos(alpha)cos(Beta) + a2sin(alpha)sin(Beta) =0 then b2prove that: tan(alpha)tan(beta)={b2(x2 - a2)}/{a2(y2- b2)}

1 Answers

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IF x cos(alpha)+ ysin(alpha)=1,
a b
xcos(Beta) + ysin(Beta)=1 and
a b
cos(alpha)cos(Beta) +
a²
sin(alpha)sin(Beta) =0 then
b²
prove that:
tan(alpha)tan(beta)={b²(x²- a²)}/{a²(y²- b²)}