HIGHER SECONDARY FIRST YEAR MATHEMATICS. TRIGONOMETRY Creative Questions Time : 1.15 Hrs Marks : 45 Part - I Choose the correct answer 10 1 = 10

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1 HIGHER SECONDARY FIRST YEAR MATHEMATICS TRIGONOMETRY Creative Questions Time :. Hrs Marks : Part - I Choose the correct answer. If cos x, then x a) n b). The domin of the function y x a) (n ) c) y b), c), tan. The value of tan (n ) d) n d) y a) b) c) d). If is the root of cos cos, then a) b) c) d) 8 8. The expression tan A cot A can be written as cot A tan A a) Acos A b) sec AcosecA c) tan A cot A d) sec A coseca. The number of values of x in the interval, x x is satisfying the equation a) b) c) d). If A lies in the third quadrant and tan A then A A cos A a) b) c) 8. The value of tan () cos is equal to d) 8 a) b) c) d)

2 9. If cos is equal to. If a) cos b) A B then tan Atan B c) a) b) c) d) cos d) Part - II Answer any three of the following questions. Find the value of. If x cosec then find the value of x. Prove that sec cot. Show that tan cot cos ec sec. If cos B tan A prove that A B B Part - III Answer any three of the following questions 9. Solve: tan ( x) tan ( x) x x. Prove that tanx cos x cosx 8. The minute hand of a watch is. cm long. How far does its tip move in minutes? (.) 9. Prove that cos cos cos n. If tan tan tan... tan then find the n.

3 Part - IV Answer any four of the following questions. Solve: x x x. An aeroplane flying with uniform speed horizontally one kilometer above the ground is observed at an elevation of.. After seconds if the elevation is observed to be. then find the speed of the planes.. Let cos( ) and let ( ), where, then find tan. In a PQR, if P cosq and Q cos P then find the angle R.. If A B C, prove that A B C A BC ***** T. Ayyanar, M.Sc., B.Ed., D.P.Tech Instructor (Mathematics) SBGGHSS, Puducherry akarthik@gmail.com Cell: 89

4 Q.No Options b b c b b d HIGHER SECONDARY FIRST YEAR MATHEMATICS TRIGONOMETRY Creative Questions Answers and Solutions Part - I a 8 c 9 c b. or ( 8 ) Part II. x cosec x

5 x cos x x x x. sec cot. tan cot tan cot cos ec sec tan sec cot cos ec. tan A B B cos B B tan A cos B tan A tan B A B A B

6 . tan ( x) tan ( x) x x tan ( x)( x) ( x x x x tan ) Part III tan x tan y tan x y xy C D C D C D cos. C D C D cosc cos D cos cos x x x x cos x x x x cos cos x cos x cosx cos x tanx 8. In minutes, the minute hand of a watch completes one revolution. Therefore in minutes, the minute hand turns through of a revolution. Therefore hence the required distance travelled is given by length l r..8 cm

7 9. Multiply and divide by cos cos cos cos cos cos convert into sum. Rearranging the terms ( tan )( tan ) ( tan )( tan ) ( tan )( tan )... ( tan ) n ( tan tan tan tan )( tan tan tan tan )...( tan ) Note ( tan tan )( )...( ) n tan( ) tan tan ( terms) n tan tan tan tan n tan tan tan tan n

8 Part IV. x x x x x x x x x x cos x x cosx x x(cos x ) x cosx x n General solution x n ( ) x n, n Z cos x x General solution x n x n, n Z. O is the point of observation and A, B are two positions of Aeroplane Given AOD, BOD AC km Now AOB ABO AB OA In OAC, AC OA A ( B OA OA km km ) O C D ) ) AB km Time to cover the distance AB seconds or hr Speed of the Aeroplane dis tance time

9 km / hr. Given cos( ) ( ) tan( ) tan ( ) ( ) ( ) cos( ) tan( ) tan tan ( ) ( ) tan( ) tan( ) tan( )tan( ) tana tanb tan( A B) tanatanb 8. P cosq Squaring on both sides P cosq 9 P cos Q P cosq Q cos P Squaring on both sides Q cos P Q 9cos P Q cos P

10 adding and 9 P cos Q P cosq P cosq cos P Q 9 ( P Q) ( P Q) ( P Q) principal value General solution P Q n P Q n ( ), n Z Q 9cos possible values are P Q, In a right angle triangle one of the angle should be 9 P Q cos P ( A B) Acos B cos A B P Q R. ( A B) C ( A B)cos( A B) C ( C )cos( A B) C C cos( A B) C cos C Ccos( A B) cosc Ccos( A B) cos( ( A B) Ccos( A B) cos( A B) C A B A BC T. Ayyanar, M.Sc., B.Ed., D.P.Tech Instructor (Mathematics) SBGGHSS, Puducherry akarthik@gmail.com Cell: 89