54. If sin "G47) -cos %) = 2 Tan's,...
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54. If sin "G47) -cos %) = 2 Tan's, then x = a + b a) 1 -- ab a-b 1 + ab 22+52 a?- b2 c) 1-a2b2 d) T-a?? 55. For any two nonempty sets A and B, which of following is true ? a) (AB) 8 A C. (A - B) SA b) A8 (AUB) dy A8 (A-B) ondo R-

11th - 12th Class
Maths
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( sin 2 A=frac{2 tan A}{1+tan ^{2} A} quad ) and ( quad cos 2 beta=frac{1-tan ^{2} B}{1+tan ^{2} B} ) to lan ( A=a ) and ( tan B=b ) ( therefore quad sin ^{-1}left(frac{2 a}{1+a^{2}}right)=2 A quad ) and Eo ( 2 B=cos ^{-1}left(frac{1-b^{2}}{1+b^{2}}right) ) ( therefore quad 2 A-2 B=2 tan ^{-1} x ) ( begin{aligned} Rightarrow frac{t}{t} x &=tan (A-B) &=frac{tan A-tan B}{1+tan A tan B}=frac{a-b}{1+a b} end{aligned} )
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