Question

If Asin theta = 3 and Acos theta =4 find the values of À and theta

Answer 1

Answer:

A cos theta + B sin theta = 4

[A cos theta + B sin theta]^2 = 16 ……….i

A sin theta - B cos theta = 3

[A sin theta - B cos theta]^2 = 9 ………….i i

Adding equation i and ii we get,

(A cos theta)^2 + (B sin theta)^2 + (A sin theta)^2 + (B cos theta)^2 + 2 AB cos theta sin theta - 2 AB cos theta sin theta = 25

A^2[(cos theta)^2 + (sin theta)^2] + B^2[(cos theta)^2 + (sin theta)^2] = 25

A^2 + B^2 = 25