If cos x cos y = n, sin x sin y = m...
Question
If cos x cos y = n, sin x sin y = m, then what is (m2−n2)sin2y equal to?
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If ( frac{cos x}{cos y}=n, frac{sin x}{sin y}=m, ) then what is ( left(m^{2}-n^{2}right) sin ^{2} y ) equal to?
(a) ( 1-n^{2} )
(b)1 + n^{2}
(c) ( m^{2} )
(d) ( n^{2} )

11th - 12th Class
English
Solution
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If cos x cos y = n, sin x sin y = m, then what is (m2−n2)sin2y equal to?
Fullscreen

( frac{cos x}{cos y}=n, frac{sin x}{sin y}=m )
( cos x=n cos y ; sin x=m sin y )
( sin ^{2} x+cos ^{2} x=1 )
( =sin ^{2} x^{2} sin ^{2} y+n^{2} cos ^{2} y=1 )
( Rightarrow m^{2} sin ^{2} y+n^{2}left(1-sin ^{2} yright)=1 )
( =1left(m^{2} sin ^{2} x+n^{2}-n^{2} sin ^{2} y=1right. )
( Rightarrowleft(m^{2}-n^{2}right) sin ^{2} y=1-n^{2} )

option (a)

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