Question

If θ + θ = and θ − θ = ,then show that a 2+b 2=m2+n 2 .​

Answer 1

Answer:

Step-by-step explanation:

Given, a cos θ + b sin θ = m …(1) a sin θ – b cos θ = n …(2) Squaring and adding equation 1 and 2, we get – (a cos θ + b sin θ)2 + (a sin θ – b cos θ)2 = m2 + n2 ⇒ a2cos2θ + b2sin2θ + 2ab sin θ cos θ + a2sin2θ + b2cos2θ - 2ab sin θ cos θ = m2 + n2 ⇒ a2cos2θ + b2sin2θ + a2sin2θ + b2cos2θ = m2 + n2 ⇒ a2(sin2θ + cos2θ) + b2(sin2θ + cos2θ) = m2 + n2 Using: sin2θ + cos2θ = 1, we get – ⇒ a2 + b2 = m2 + n2