NCERT Solutions for Class 10 Maths

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Introduction to Trigonometry

Exercise 1

1.   In Δ ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine:

(i) sin A cos A     (ii) sin C cos C

2.   In adjoining figure, find tan P – cot R :

3.   If sin A =  calculate cos A and tan A.

4.   Given 15 cot A = 8, find sin A and sec A.

5.   Given  calculate all other trigonometric ratios.

6.   If ∠ A And ∠ B are acute angles such that cos A= cos B, then show that ∠ A = ∠ B.

7.   If  Evaluate:

8.   If 3 cot A= 4, check whether

9.   In Δ ABC right angles at B, if  find value of:

(i) sin A cos C + cos A sin C      (ii) cos A cos C – sin A sin C

10.  In Δ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

11.   State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1.

(ii)  for some value of angle A.

(iii) cos A is the abbreviation used for the cosecant of angle A.

(iv) cot A is the product of cot and A.

(v)  for some angle θ.

Exercise 2

12.  Evaluate:

13.  Choose the correct option and justify:

(A) sin 600       (B) cos 600          (C) tan 600           (D) sin 300

(A) tan 900       (B) 1                       (C) sin 450           (D) 0

(iii) sin 2 A = 2 sin A is true when A =

(A) 0                   (B) 300                  (C) 450                 (D) 600

(A) cos 600       (B) sin 600          (C) tan 600           (D) None of these

14.  If 0< A + B 900 ≤ A > B, find A and B.

15.  State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B

(ii) The value of sin θ increases as θ as increases.

(iii) The value of cos θ increases as θ as increases.

(iv) sin θ = cos θ for all values of θ.

(v) cot A is not defined for A = 00.

Exercise 3

16.  Evaluate:

17.  Show that:

(i)  tan 480 tan 230 tan 420 tan 670 = 1

(ii) cos 380 cos 520 – sin 380 sin 520 = 0

18.  If tan 2A = cot (A – 180) where 2A is an acute angle, find the value of A.

19.  If tan A = cot B, prove that A + B = 900.

20.  If sec 4A = cos ec (A- 200) , where 4A is an acute angle, find the value of A.

21.  If A, B and C are interior angles of a Δ ABC, then show that

22.  Express sin 670 + cos 750 in terms of trigonometric ratios of angles between 00 and 450.

Exercise 4

23.  Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

24.  Write the other trigonometric ratios of A in terms of secA.

25.  Evaluate:

26.  Choose the correct option. Justify your choice:

(i)   9 sec2 A – 9 tan2 A =

(A) 1             (B) 9            (C) 8            (D) 0

(ii)   (1+ tan θ + sec θ) (1 + cot θ – cos ecθ) =

(A) 0             (B) 1             (C) 2            (D) None of these

(iii) (sec A + tan A) (1 – sin A) =

(A) sec A       (B) sin A    (C) cos ecA   (D) cos A

(iv)

(A) sec2 A     (B) -1           (C) cot2 A    (D) None of these

27.  Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

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