Question

if a cos theta + b sin theta = m and a sin theta - b cos theta =n then prove that a square + b square = m square + n square ​

Answer 1

Step-by-step explanation:

NOTE :

HERE ^ MEANS POWER FUNCTION FOR EX. M^2 MEANS

=. M SQUARE

a cos theta + b sin theta = m

a sin theta - b cos theta =n

square bothe equation and add

(a cos theta + b sin theta)^2 = m^2

(a sin theta - b cos theta)^2 =n^2

a^2 (cos theta)^2 + b^2 (sin theta)^2 + 2×a×b (sin theta)× ( cos theta)=m^2

b^2 (cos theta)^2 + a^2 (sin theta)^2 - 2×a×b (sin theta)× ( cos theta)=n^2

【 add both and taking same sine same side】

a^2【cos theta^2 + sin theta ^2】 + b^2【cos theta^2 + sin theta ^2】 +2×a×b (sin theta)× (costheta) -2×a×b (sin theta)× (costheta) = m^2 +n^2

because 【({{ cos theta^2+ sin theta^2 =1 )}】

then.....

a^2+ b^2 = m^2 + n^2