Question

if X=3sin theta + 4cos theta and y equals to 3cos theta -4 sin theta then prove that x2+y2=25​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given:

$x=3 sin$θ$+4cos$θ

$y=3cos$θ$-4sin$θ

To prove:

$x^2+y^2=25$

Solution:

Taking the left-hand side,

$x^2+y^2$

Putting the respective values,

$=(3sin$θ$+4cos$θ$)^2$+$(3cos$θ$-4sin$θ$)^2$

=$9sin^2$θ+$16cos^2$θ+$24sin$θ$cos$θ+$9cos^2$θ+$16sin^2$θ-$24sin$θ$cos$θ

=$9(sin^2$θ+$cos^2$θ$)+16(sin^2$θ+$cos^2$θ)

We know that,

$sin^2$θ$+cos^2$θ=1

So,

=$9+16$

=25=right-hand side

Hence, proved that $x^2+y^2=25$.