Question

solve the equation ; x sin theta +y cos theta =a and x cos theta - y sin theta =b​

Answer 1

Answer:

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Answer 2

Answer:

{ Note ; considering theta as @}

The given pair of linear equations are;

xsin@ + ycos@ = a ------(1)

and xcos@ - ysin@ = b -------(2)

Now,

Multiplying eq-(1) with sin@ and eq-(2) with cos@ ,

We get,

x(sin@)^2 + ysin@•cos@ = asin@ -----(3)

and,

x(cos@)^2 - ysin@•cos@ = bcos@ -----(4)

Now,

Adding eq-(3) and (4) ,

we get;

=> x(sin@)^2 + ysin@•cos@ + x(cos@)^2

–ysin@•cos@ = asin@ + bcos@

=>x{(sin@)^2+(cos@)^2}=asin@+bcos@

=> x = asin@ + bcos@.

Now,

Multiplying eq-(1) with cos@ and eq-(2) with sin@ ,

We get,

xsin@•cos@ + y(cos@)^2 = acoa@ ----(5)

and

xsin@•cos@ - y(sin@)^2 = bsin@ -----(6)

Now,

Subtracting eq-(6) from eq-(5)

We get;

=>xsin@•cos@+y(cos@)^2-xsin@•cos@

+ y(sin@)^2 = acos@ - bsin@

=> y{(sin@)^2 +(cos@)^2}=acos@-bsin@

=> y = acos@ - bsin@

Thus , the required values are;

x = asin@ + bcos@

y= acos@ - bsin@