Question

x=asin0 + bcos0
y=acos0 + asin0
x2 - y2=a2 + b2​

Answer 1

Answer:

x = a sin theta + b cos theta,

y = a cos theta + b sin theta

LHS : x2 + y2 = ( a cos theta + b sin theta )2 + ( a sin theta + b cos theta )2

➪ a2 cos2 theta + b2 sin2 theta - 2ab sin theta. cos theta + a2 sin2 theta + b2 cos2 theta + 2ab sin theta. cis theta

➪ a2 (cos2 theta + sin2 theta) + b2(sin2 theta + cos2 theta)

➪ a2 +b 2

Hence, a2+ b2 = x2 + y2 proved.

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Answer 2

x = a sin theta + b cos theta

y = a cos theta + b sin theta

LHS : x2 + y2 =

( a cos theta + b sin theta )2 + ( a sin theta + b cos theta )2

➪ a2 cos2 theta + b2 sin2 theta - 2ab sin theta.

cos theta + a2 sin2 theta + b2 cos2 theta + 2ab sin theta. cis theta

➪ a2 (cos2 theta + sin2 theta) + b2(sin2 theta + cos2 theta)

➪ a2 +b 2

Hence, a2+ b2 = x2 + y2 proved.

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