If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that m2 + n2 = a2 + b2
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If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that m2 + n2 = a2 + b2
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that m2 + n2 = a2 + b2
Given,
m2 = a2 cos2 θ + 2 ab sin θ cos θ + b2 sin2θ
and
n2 = a2 sin2 θ-2 ab sin θ cos θ + b2cos2 θ
Adding equations (i) and (ii)
m2 + n2 = a2 (cos2 θ + sin2 θ) + b2(cos2θ + sin2 θ)
= a2 (1) + b2 (1)
= a2 + b2 = RHS