Question

A-4.a If a cos theta + b sin theta= 3 & a sin theta -b cos theta = 4 then value of a2 + b2 is
(1) 25
(2) 14
(3) 7​

Answer 1

Step-by-step explanation:

⇒  acosθ+bsinθ=4     --- ( 1 )

⇒  asinθ−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]