Support the Monkey! Tell All your Friends and Teachers

Help / FAQ


SUPPLEMENTARY PROBLEMS

1. Prove the following

  1. = 2 cosec A   
  2. sec6A - tan 6A = 1 + 3tan2A + 3 tan4A

  3. (1+ sin + cos ) 2 = 2 (1 + sin ) (1 + cos )    
  4. sin 6 + cos6 = 1 - 3cos2 + 3 cos4

  5. sin x ( cot x + 3 ) ( 3 cot x + 1 ) = 3 cosec x + 10 cos x

  6. If x = a cos2 + b sin2 prove that (x- a ) (b - x ) = ( a - b )2 sin2 cos2

  7. If sin = Find cos and cot

  8. ( sin - cos ) ( sin + cos ) = - cos2

  9. (tan2A - cot A)2= tan 4A - 2 tan 2A cot A + cot2A

  10. sec - sec sin2 = cos

  11. tan A sin A + cot A cos A = ( sec A + cosec A) (sec A. cosec A - 1) . sin A cos A

2. Verify the identity.

  1. tan - csc sec ( 1 - cos2) = cot

  2. (x sin - y cos )2 + (x cos + y sin ) = x2+ y2

3. Find the values of t- ratios of , given that tan = 5/4

Ans. Quad. I:-

Quad III:-

4.

  1. Prove that

  2. Prove that

  3. Prove that

  4. Prove that cos 2250 x cos 6750 + sin 5850
    sin 3150 = 0

  5. Evaluate

  6. Prove that sin 200 sin 400sin 600sin 80 0 = 3/6 ( Don't use calculator or table)

  7. Show that sin a sin (60 0 - a) sin ( 600 + a) = 1/4 sin 3a

  8. Prove that

  9. Prove that

  10. 1) If sin 3a = 0.4 Find cos 3a

    2) Find sin a if tan a /2 = 1/

  11. Prove that (cos A - cos B) 2 + (sin A - sin B)2 = 4 sin 2

  12. If A + B + C = 180 0 Prove that cos A+ cos B - cos C = 4 cos A/2 cos B/2 sin C/2 -1

  13. When A + B + C = 1800, show that sin 2A + sin 2B + sin 2C = 4 sin A . sin B sin C

5. Find the values of sin (a + b), cos (a + b) and tan (a + b), given

  1. sin a = 8/17, tan b= 5/12 a , and b in Quad I.

    Ans. 171/221, 140/221, -63/16

  2. sin a = 1/3, sin b = 2 /5, a in Quad I b in Quad II,

    Ans.

6. Find the values of sin ( a - b ) , cos (a - b) and tan (a - b ) given

  1. cos a = -12/13 , cot b = 24/7, a in Quad. II, b in Quad I

    Ans. 204/325, -253/325, 21/220

  2. sin a = 1/3, sin = 2/5, a in Quad. II, b in Quad I

Ans.

7. Prove that tan (450+ q) =

  1. sin (a + b) sin (a - b) ) = sin2a - sin2b) and sin (a + b) ) sin (a -b) ) = cos2b - cos2a

  2. sin 500 - cos 80 0 = cos 700
  3. sin 400 - cos 700 = cos 800

  4. cos 200 cos 400 cos 600 cos 800 = 1 / 16
  5. sin 750 - cos 150 = cos 1050 + sin 150

  6. cos2x + cos2(x +1200) + cos2(x - 1200) = 3/2.

8. Find the values of sin 2 , cos 2 and tan 2 ; given

  1. sin = 3/5, is in Quad. I

    Ans. 24/25, 7/25, 24/7

  2. tan = - 1/5, is in Quad. II

    Ans. - 6/13, 12/13, - 5/12

  3. Prove that 2 using x=300

  4. Prove that using A = 600

9. Find the maximum and minimum value of each sum and value of x or t between 0 x or t 1800

  1. 4 cos x + 3 sin x into the form (sin (x-a))
    Ans. max. 5 when x = 36 0 22'
    min -5 when x = 216 0 52'

  2. 5 cos 3t + 12 sin 3t into the form cos (3t - a)
    Ans . max 13 when t = 220 38'
    min -13 when t = 82038'

*******

[next page]

Index

Trignometric Identities

4.1 Fundamental Identities
4.2 The addition formulas
4.3 The multiple-angle (Double & Half angle) formulas
4.4 Tangent Identities
4.5 Factorization & Defactorization

Supplementary Problems


Chapter 5

All Contents Copyright © All rights reserved.
Further Distribution Is Strictly Prohibited.


Search:
Keywords:
In Association with Amazon.com