PUIYearTrigonometryVikasana - CET 2012Remember:1. Angle between Minute hand1. Angle between Minute hand and Hour hand in X Hr. andY min.11is 30X- Y is 30X- Y2Vikasana - CET 20122 22. The maximum value ofC S + + + +2 22 2aCos bSin c, isc a b and th i i lib +2 2the minimum value isc a bVikasana - CET 20122 2 2 23If C AC B 1 Si ASi B + = = ++ =2 2 2 23. If Cos ACos B 1 Sin ASin B then A B.2+ =24. If aSinx bCosx c, then = + 2 2 2bSinx -aCosxa b cVikasana - CET 20121. The angle between Hr.hand andgMin. hand of a clock when the timei3 20 is 3: 20 11) 102) 203)304)22 1) 102) 203)304)222Vikasana - CET 2012=11Solution: Req. 30(3)- (20)2= = 2 90 - 110 20 = = 90 - 110 20 Ans:(2) Ans:(2)Vikasana - CET 20122. The vertical angle of an isoscelestriangle is 45then the base angle in circ lar meas re is in circular measure is 3 3(1) 6730 (2) 6530 (3)(4) 3 3(1) 6730 (2) 6530 (3)(4) 816Vikasana - CET 2012+ + = Solution: A B C 180+ = = =A B 180-C 180-45 1353= = =3 B A2A13543 =3 A8Ans: (3)Ans: (3)Vikasana - CET 20123.If the length of a chord of a circleis equal to that of the radius of the circle, then the angle subtended in , gradians at the centre of the circle bychord is chord is 1) 12)3) 4) ) ) )2 3)4Vikasana - CET 2012Solution:OAB is an equilateral triangle = OAB is an equilateral triangleAOB 3 Ans:(3)

oABrrrBrVikasana - CET 2012+ =1 54If SinAand A is + = 4. If SinAand A isSinA 2acute then A is 1)2)3 4) 1)2) 6 4) None of these 3 4) ) None of these3Vikasana - CET 2012: Solution + = +1 1SinA2SinA 2

= =SinA 21SinA A 2 6 Ans: (1) 2 6Vikasana - CET 2012 5 If S t 2thth + = 5.If Sec tan 2, then thevalues of Sec& tan are respectively,, , 1 2 5 3 2 11)2)3) 4)None4 3 4 4 3 4 4 3 4 4 3 4Vikasana - CET 2012: Solution =1Sec - tan2( )( ) 1 + = Q2Sec tan Sec tanadding and Simplifying5 3 = =5 3Secand tan4 4Ans: (2)Vikasana - CET 20126. The value of +2 2Cos 85 Cos 5, is,11)0 2) 13)14) 1)0 2) - 13)14)2Vikasana - CET 2012: AB 1 Solution + =2 2Cos Cos+ = when A B 90 Ans.(3)1Vikasana - CET 20127The maximum value of + +7. The maximum value of4Sin 3Cos 2, is + + 4Sin 3Cos 2, is1)7 2)4 3)64)5 ) ) ) )Vikasana - CET 2012: Solution = + +22Max.value c a b= + + = 2 16 9 7Ans.(1)7Vikasana - CET 2012 + = 8Sin Cos 1 + ==8. Sin Cos 1, then Sin2 then Sin21)1 2) - 1 3)04)2Vikasana - CET 2012:1Solution 2 2 Sq. both sides,Sin Cos 2Sin Cos 1 + + = =2 2Sin Cos 2Sin CosSin2 0 Ans.(3)0Vikasana - CET 2012 9If Cos +Sec 2then the = 9. If Cos +Sec 2, then the100 100 = value of Cos Sec1)0 2)13)2 4) - 11)0 2)13)2 4) 1Vikasana - CET 20121Solution: Cos + = 1 + 1CosCos Cos = 1 = Sec G.E. = 1-1 = 0Vikasana - CET 2012 = 10. If Sec +tan 4 then Cos =8 15 8 7 1) 2) 3) 4)1) 2) 3) 4)15 17 17 17Vikasana - CET 2012 1S l tiS t = Solution: Sec tan411adding, we get 2Sec =4+417 17Sec =88 8Cos =17Vikasana - CET 2012 11The value of tan20+tan40 11. The value of tan20+tan40, + tan60 + ... +tan180is1)02)13)2 4)4 1)02)13)2 4)4Vikasana - CET 2012: Solution If A+B =180then tanA=-tanB or tanA+tanB=0t 20+t 160+t 40+ tan20+tan160+tan40+tan140+...+tan180=0+0+... =0 :(1) Ans 0Vikasana - CET 201212 The value of 2 2212.The value ofSin tanC) + ++ +22 2Cos1 Cot (1 tan1) - 1 2)03)1 4)2 1) 1 2)03)1 4)2Vikasana - CET 2012: Solution Put = 45 : Solution Put = 4511 1221 12G.E. =+ +1+1 (1+1) 2=1Ans: (3) 1 Ans: (3) 1Vikasana - CET 201213. A,B,C are the angles of a13. A,B,C are the angles of aABC, then 3A+2B+C A- CCos +Cos =2 2 2 21)12)0 3)CosA4)CosCVikasana - CET 2012Sl ti Put A=B=C : Solution Put A=B=CG.E. =Cos180+Cos0=-1+1=0Ans: (2) 0 Ans: (2) 0Vikasana - CET 2012 14. If x=Cos1and y=Cos1 14. If x=Cos1and y=Cos1then1) x=y 2) xy4) 2x=yVikasana - CET 2012Sl Cid i : Solution Cosis decreasingf0< < for 0< Cos1 Cos1 >Cos1Ans: (3)x > y ( ) yVikasana - CET 2012 15In aABCC=90 then 15. In aABC, C=90 ,thenthe equation whose roots 2 2 2 2B are tanA & tanis2 2 2 22 2 2 2+ + 1)abx c x + ab = 02)abx c x - ab = 03)abx c x ab = 03)abx c x + ab = 0 3)abx - c x - ab = 03)abx - c x + ab = 0Vikasana - CET 2012: Solution C=90 A+B=902 2 2(a +b = c )t At B=1 =1 tanAtanB=1 =1a bt A t B +a b+ =tanA+tanB=b a22 2 += a b -c- Ans: (4)ab abVikasana - CET 2012 ab ab16. If 5Sinx+4Cosx=3, then ,4Sinx - 5Cosx=1)4 2)4 3)3 4)2 2 2 1)4 2)4 3)3 4) Vikasana - CET 20122 2 2Sl ti G E = b2 2 2: Solution + G.E. = a b - c== = 16+25- 9 32 4 2Ans: (2)( )Vikasana - CET 2012 17. If a=Sin1and b=Sin1th then 1)a=b2)ab 4)a=2bVikasana - CET 2012: SolutionSin is increasing gin 0< y>z 3)x=y>z4)x