Q. 215.0( 9 Votes )

If a cos <span la A. m2 n2

B. m2n2

C. n2 m2

D. m2 + n2

Answer :

Given: a cos θ + b sin θ = m

Squaring both sides, we get


(a cos θ + b sin θ)2 = m2


a2 cos2 θ + b2 sin2 θ + 2ab cos θ sin θ = m2 ……(i)


And a sin θ – b cos θ = n


Squaring both sides, we get


(a sin θ – b cos θ)2 = n2


a2 sin2 θ + b2 cos2 θ – 2ab sin θ cos θ = n2 ……(ii)


To find: a2 + b2


Adding (i) and (ii), we get


a2 cos2 θ + b2 sin2 θ + 2ab cos θ sin θ + a2 sin2 θ + b2 cos2 θ – 2ab sin θ cos θ = m2 + n2


a2 (cos2 θ + sin2 θ) + b2 (sin2 θ + cos2 θ) = m2 + n2


a2 + b2 = m2 + n2 [ sin2 θ + cos2 θ = 1]

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