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# ( * )If ax / cos theta + by /sin theta  = a square – b square and ax sin theta / cos square theta – by cos theta / sin square theta = 0 then (ax)^2/3 + (by)^2/3 =

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
Hello student, Please find the answer to your question below
ax / cosØ + by /sinØ = a2 – b2
ax sinØ / cos 2Ø – by cosØ / sin 2 Ø = 0

Equation numner is 2 is not proper...
Please send the correct question
Piyush
15 Points
8 months ago
From the second relation
axsinø/cos²ø - bycosø/sin²ø = 0
axsin³ø-bycos³ø/cos²øsin²ø = 0
axsin³ø-bycos³ø=0
axsin³ø=bycos³ø
tan³ø=by/ax
tanø=by^1/3/ax^1/3
sinø=by^(1/3)/[(ax)^2/3 + (by)^2/3]^1/2
( By using 2tanø/2/1+tanø/2 for sinø )
Similarly cosø=(ax)^1/3/[(ax)^2/3 + (by)^2/3]^1/2
( By using 1-tan²ø/2/1+tan²ø/2 )
Put sinø and cosø in 1st relation
Answer is : (a²-b²)^2/3