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If cosø+ b sinø =m and simø-b cosø=n,p.t.Asqare +bsqare =m square-n square

If cosø+ b sinø =m and simø-b cosø=n,p.t.Asqare +bsqare =m square-n square

Grade:10

1 Answers

somi teez
105 Points
6 years ago
hi,
your question is little wrong  it should be  
a cosø+ b sinø =m and a sin ø-b cosø=n,Asqare +bsqare =m square + n square
i think you just need a hint....then you may solve it 
to get ,  m^2 +n ^2
calculate m^2 =(acosø+ b sinø)^2
                    =acos ^2  ø+ b sin ^2ø  + 2 * acosø* b sinø
now ,
calculate n^2 =a sin ^2 ø +b cos ^2 ø  – 2 *a sin ø*b cosøm ^2 + n^2 =a^2 cos^2 \Theta +b^2 sin^2 \Theta +2*a cos \Theta *b sin \Theta +a^2 sin^2 \Theta + b^2 cos ^2 \Theta - 2a sin ø*b cosø
so, 
                        =a^2 cos^2 \Theta +b^2 sin^2 \Theta +a^2 sin^2 \Theta + b^2 cos ^2 \Theta
                        =a^2( cos^2 \Theta + sin^2 \Theta) +b^2 (sin^2 \Theta + cos ^2 \Theta) =(a^2 + b^2 ) (sin ^2 \Theta + cos ^2 \Theta )
                       =  a^2 + b^2 ….........proved 
if you got it then approve 
 
 
 

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