queries-from-fb-maths

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Q. If x=acos^3&curren;sin^2&curren; , y=asin^3&curren;cos^2&curren; and (x^2+y^2)^p/(xy)^q (p,q belongs to N) is independent of &curren;,then find value of p and q.

Amit Saxena · Accepted Answer

x^2 = a^2 cos ^6 x * sin^4 x
y^2 = a^2 sin ^6 x * cos ^4 x

adding them we get a^2 sin ^ 4 x * cos ^ 4 x applying trigonometric identities

xy = a ^ 2 cos ^ 5x sin ^ 5 x

now putting it in the expression

we get

(sin 2x)^(4p - 5q) ignoring the constants and applying trigonometric identities

now the expression has to be independent of x

so put 4p - 5q = 0

so p/q = 5/4

now p , q are natural numbers

p = 5t , q = 4 t

where t belongs to positive integers

will be the set of values of p,q

IIT JEE Entrance Exam> queries-from-fb-maths...

Q. If x=acos^3¤sin^2¤ , y=asin^3¤cos^2¤ and (x^2+y^2)^p/(xy)^q (p,q belongs to N) is independent of ¤,then find value of p and q.

Radhika Batra , 11 Years ago

Amit Saxena

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IIT JEE Entrance Exam> queries-from-fb-maths...

Q. If x=acos^3¤sin^2¤ , y=asin^3¤cos^2¤ and (x^2+y^2)^p/(xy)^q (p,q belongs to N) is independent of ¤,then find value of p and q.

Radhika Batra , 11 Years ago

Amit Saxena

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

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