## Chapter 5 Trigonometric Ratios R.D. Sharma Solutions for Class 10th Math Exercise 5.1

Exercise 5.1

1. In each of the following one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

(i) sinA = 2/3

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(ii) cosA = 4/5

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(iii) tanÎ¸ = 11

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(iv)  SinÎ¸ = 11/5

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(v) tanÎ± = 5/12

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(vi) SinÎ¸ = √3/2

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(vii) CosÎ¸ = 7/25

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(viii) tanÎ¸ = 8/15

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(ix) cotÎ¸ = 12/5

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(x) secÎ¸ = 13/5

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(xi) cosecÎ¸ = √10

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(xii) cosecÎ¸ = 12/5

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2. In a ∆ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine
(i) Sin A, Cos A
(ii) Sin C, cos C

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3. In Fig below, Find tan P and cot R. Is tan P = cot R ?

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4. If sinA = 9/41, compute cosA and tanA.

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5. Given 15 cot A = 8, find SinA and SecA .

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6. In ∆PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.

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7. If cot Î¸ = 7/8 , evaluate :
(i) (1+sinÎ¸)(1-sinÎ¸)/(1+cosÎ¸)(1-cosÎ¸)
(ii) cot2Î¸

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(i)

(ii)

8. If 3 cot A = 4, check whether 1-tan2 A/1+tan2 A = cos2 A - sin2 A or not.

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9. If tan Î¸ = a/b , find the value of cosÎ¸ + sinÎ¸/cosÎ¸ - sinÎ¸

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10. If 3 tan Î¸ = 4 , find the value of 4cosÎ¸ - sinÎ¸/2cosÎ¸ + sinÎ¸

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11. If 3 cot Î¸ = 2 , find the value of 4 sinÎ¸ - 3 cosÎ¸/2 sinÎ¸ + 6 cosÎ¸

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12. If tan Î¸ = a/b , prove that a sin Î¸ - b cos Î¸/a sin Î¸ + b cos Î¸ = a2 - b2/a2 + b2 .

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13. If sec Î¸ = 13/5, show that 2cos Î¸ - 3cos Î¸/4sin Î¸ - 9cos Î¸ = 3.

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14. If cos Î¸ = 12/13, show that sin Î¸ (1 - tan Î¸) = 35/156 .

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15. If cot Î¸ = 1/√3 , show that  1- cos2  Î¸/2 - sin2 Î¸ = 3/5 .

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16. If tan Î¸ = 1/√7 cosec2 Î¸ - sec2  Î¸/cosec2 Î¸ + sec2  Î¸ = 3/4 .

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17. If Sec Î¸ = 5/4 , find the value of sin Î¸ - 2 cos Î¸/ tan Î¸ - cot Î¸

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18. If tan Î¸ = 12/13, find the value of 2 sin Î¸ cosÎ¸/cos2 Î¸ - sinÎ¸

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19. If cos Î¸ = 3/5 , find the value of sinÎ¸ - (1/tanÎ¸)/2 tan Î¸

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20. If sin Î¸ = 3/5 , evaluate cosÎ¸ - (1/tanÎ¸)/2 cot Î¸

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21. If tan Î¸ = 24/7 , find that sin Î¸ + cos  Î¸

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22. If sin Î¸ = a/b , find sec Î¸ + tan Î¸ in terms of a and b .

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23. If 8 tan A = 15, find sin A - cos A .

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24. If tan Î¸ = 20/21, show that 1-sin Î¸ + cos Î¸/1+ sin Î¸ + cos Î¸ = 3/7  .

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25 . If cosec A = 2 find 1/Tan A + sin A/1+cos A

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26. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

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27. In a ∆ABC, right angled at A, if tan C = √3, find the value of sin B cos C + cos B sin C.

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28. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) Sec A = 12/5 for some value of angle A.
(iii) Cos A is the abbreviation used for the cosecant of angle A.
(iv) Sin Î¸ = 4/3 for some angle Î¸ .

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29. If sin Î¸ = 12/13 find sin2Î¸ - cos2Î¸/2 sinÎ¸ cosÎ¸ × 1 tan2Î¸  .

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30. If cos Î¸ = 5/13 find sin2Î¸ - cos2Î¸/2 sinÎ¸ cosÎ¸ × 1 tan2Î¸ .

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31.  If sec A = 5/4, verify that 3 sinA - 4 sin3A/4 cos3 A - 3 cosA = 3 tan A - tan3 A /1 - 3 tan2A  .

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32.

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33. If sec A = 17/8 , verify that 3-4 sin2 A/4 cos2 A-3 = 3-tan2 A/1-3 tan2 A.

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34.

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35. If  3 cos Î¸ - 4 sin Î¸ = 2 cos Î¸ + sin Î¸, find tan Î¸.

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36. If ∠A and ∠P are acute angles such that tan A = P, then show that ∠A = ∠P.

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