Question

If acosθ + bsinθ = 4 & asinθ - bcosθ = 3, then a²+b² = *​

Answer 1

Answer:

25

Step-by-step explanation:

acosθ+bsinθ=4     --- ( 1 )

⇒  a sinθ−bcosθ=3      ---  ( 2 )

→   Now, squaring and adding ( 1 ) and ( 2 )

∴   (acosθ+bsinθ)2+(asinθ−bcosθ)2=42+32

⇒  a2cos2θ+2ab.sinθcosθ+b2sin2θ+a2sin2θ−2ab.sinθcosθ+b2cos2θ=16+9

⇒  a2(sin2θ+cos2θ)+b2(sin2θ+cos2θ)=25

∴   a2+b2=25        [∵sin2x+cos2x=1]