Question

if x=acos∅ and y=asin∅, then x²y² is equal to​

Answer 1

Your answer in attachment

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Answer 2

Step-by-step explanation:

Given:-

x=acos∅

y=asin∅

To find:-

Find the value of x^2y^2?

Solution:-

Given that

x=acos∅

On squaring both sides then

=>x^2=(acos∅ )^2

x^2 = a^2 cos^2∅ ----------(1)

and

y=asin∅

On squaring both sides then

=>y^2 = (asin∅)^2

y^2 = a^2 sin^2∅------------(2)

On multiplying (1)&(2)

1)

x^2 y^2 = a^2 cos^2∅ × a^2 sin^2∅

x^2 y^2 = a^4 Sin^2∅ Cos^2∅

2)

On adding (1)&(2)

x^2+y^2 =

a^2 cos^2∅+a^2 sin^2∅

=>a^2(cos^2∅+ sin^2∅)

We know that

Sin^2 A+ Cos^2 A = 1

=>a^2(1)

=>a^2

x^2+y^2 = a^2

Answer:-

The value of x^2y^2 for the given problem is

x^2y^2=a^4 Sin^2∅ Cos^2∅

Used formulae:-

• Sin^2 A+ Cos^2 A = 1