44. If cosec-sin=3a,sec-cos=3b then 2a2b(2a+2b)

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c o s e c θ - s i n θ = a^{3}

s e c θ - c o s θ = b^{3}

a^{2} b^{2} (a^{2} + b^{2}) =

sin 3 A {cos}^{3} (B - C) + sin 3 B {cos}^{3} (C - A) + sin 3 C {cos}^{3} (A - B) = sin 3 A sin 3 B sin 3 C

{sin}^{3} A + {sin}^{3} B + {sin}^{3} C = 3 cos (A / 2) cos (B / 2) cos (C / 2) + cos (3 A / 2) cos (3 B / 2) cos (3 C / 2)

A + B + C = π

cos A + cos B + cos C

= 0 = sin A + sin B + sin C

cos 3 A + cos 3 B + cos 3 C = 1

\sqrt{3}

\Rightarrow

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