Question

if x coso -isino=a, if x coso+y sino =b, prove that x² + y^2 = a^2+b²​ ​

Answer 1

Answer:

a cosθ - b sinθ = x and a sinθ + b cosθ = y

R.H.S. = x2 + y2

= (a cosθ - b sinθ)2 + (a sinθ + b cosθ)2

= a2cos2θ - 2ab cosθ sinθ + b2sin2θ + a2sin2θ + 2absinθ cosθ + b2cos2θ

= (a2+b2) cos2θ + (b2+a2)sin2θ

= (a2+b2)cos2θ + (a2+b2)sin2θ

= (a2+b2)(cos2θ + sin2θ)

= (a2+b2) [∵ cos2θ + sin2θ = 1]

= L.H.S. ∴ a2+b2 = x2+y2.

Step-by-step explanation:

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Answer 2

Answer:

logarithms is your answer.........