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N9 (PEJ( endstream endobj 23 0 obj <> stream 2PART C(Maimum ma*s : 60)(Answer ore firll question liom each unit. Ech full question caries 15 marks.) UNIT Icosec0 cosecO........................_ + - = I sec'llcosoco -l coseco +l If tan A = 3/4, sin B = 5/13. (A lies in tlle third qua&ant ard B lies in thesecond quadrant.) Find sin (A-B) and cos (A+B). (c) Evaluate cos 570 sin 510 - sin 330 cos 390.OR I +sinA cosAProve that _...._cosA l-srnAExpress !f sin x + cos x rn the form of R sin (x + ct') where ct is acute.Prove that sin (A + B) sin (A - B) : sin' A- sil,.2 B.UNIr - IIProve that s A -- sM = tanAcos3A + cosAProve that cos 80 cos 60 cos 40 cos 20 = l/16Show that a (br + c2) cos A + b (c2 + a2) cos B + c (a' + b2) cos C = labcORp16ys th61 jg4:j3!! = 66s 24cotA+lrnAShow that sin 40 - sin 80 + sin 20 = 0Two angles of a triangular plot of land are 53" and 67" and the side betweenthern is measured io be 100cm. How many merers of fencing is required k)fence the plot ? Prove that lim x29 x-3 Marks (3+2)5 5(1 +2) Itr (a)o) IV (a)o)(c) v (a)o)(c) vl (a)o)(c) 55 555 555 vII (a) UNIT IIIEvaluate rillim lx+5 {ii) tvaluae-. r+@ X_2Find dY if (i) x aC, y = zat.dxslnlxI lr I vI + cos2x (b) (c) tf y=asinx+bcosx. 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If?Irae : 3 houn(Maximun rurks : 100) PART A(Maximun rna*s : l0)MarIsI Answer aL questions. Each question carries 2 marks.I Find trc value of tan26o + [an2 45.2. If lan 0 = 3, 6rd sm 20.l. Find the arca of a triangle given, b = 3cm, c = 2cm and A = 30".-Itor-)r x + J5 For what values of x, lhe function x2 - 5x + 6 is incrcasing ? (5x2 = lO)PART - B(Maximurn rna*s : lO)II Answer anyrr of the following quesions. Each question carries 6 ma*s.I Find the value of tan 75, witho using tables ard show lhartan 75 + cot 75 = 4.2. Thc horizrnlal distancs between two towers is 60 m and tle angle ofdepression of dre first towei as sen fiom the secqd which is in l5O mhight is 3e. Find tF height of tlte frs tower.tl Pmve rhar "o"4 * "* ts 5't 1fr6 ll *cosT- +cosT-=u4. Solve AABC, given a =,lcm, b = 5cm, c = ?cm.5 Find the second derivative of x2 log x.6. 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