Class – X Mathematics
Chapter-08 Trigonometry
(Exercise 8.1)
Questions
1. In D ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) sin Acos A (ii) sinCcosC
2. In adjoining figure, find tan P - cot R :
3. If
3
sin ,
4
A = calculate cos A and tan A.
4. Given 15cot A = 8, find sin A and sec A.
5. Given
13
sec ,
12
q = calculate all other trigonometric ratios.
6. If ÐAnd ÐB are acute angles such that cos A = cos B, then show that ÐA = ÐB.
7. If
7
cot ,
8
q = evaluate:
(i)
( )( )
( )( )
1 sin 1 sin
1 cos 1 cos
q q
q q
+ -
+ -
(ii) cot2q
8. If 3cot A = 4, check whether
2
2 2
2
1 tan
cos sin
1 tan
A
A A
A
- = -
+
or not.
9. In D ABC right angles at B, if
1
tan ,
3
A = find value of:
(i) sin AcosC + cos AsinC (ii) cos AcosC -sin AsinC
10. In D 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)
12
sec
5
A = 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)
4
sin
3
q = for some angle q .
(Exercise 8.2)
Questions
1. Evaluate:
(i) sin 60 cos30 + sin 30 cos 60 (ii) 2 tan2 45 + cos2 30 - sin2 60
(iii)
cos 45
sec30 + cos ec30
(iv)
sin 30 tan 45 cos 60
sec30 cos60 cot 45
+ - ec
+ +
(v)
2 2 2
2 2
5cos 60 4sec 30 tan 45
sin 30 cos 30
+ -
+
2. Choose the correct option and justify:
(i) 2
2 tan 30
1+ tan 30
=
(A) sin 60 (B) cos 60 (C) tan 60 (D) sin 30
(ii)
2
2
1 tan 45
1 tan 45
-
+
=
(A) tan 90 (B) 1 (C) sin 45 (D) 0
(iii) sin 2A = 2sin A is true when A =
(A) 0 (B) 30 (C) 45 (D) 60
(iv) 2
2 tan 30
1- tan 30
=
(A) cos 60 (B) sin 60 (C) tan 60 (D) Non e of these
3. If tan ( A+ B) = 3 and ( ) 1
tan ; 0 90 ; ,
3
A- B = < A+ B £ A > B find A and B.
4. State whether the following are true or false. Justify your answer.
(i) sin ( A+ B) = sin A+ sin B
(ii) The value of sinq increases as q increases.
(iii) The value of cosq increases as q increases.
(iv) sinq = cosq for all values of q .
(v) cot A is not defined for A = 0 .
(Exercise 8.3)
Questions
1. Evaluate:
(i)
sin18
cos 72
°
°
(ii)
tan 26
cot 64
°
°
(iii) cos 48° -sin 42° (iv) cos ec31° -sec59°
2. Show that:
(i) tan 48° tan 23° tan 42° tan 67° =1
(ii) cos38°cos52°-sin 38°sin 52° = 0
3. If tan 2A = cot ( A-18°), where 2A is an acute angle, find the value of A.
4. If tan A = cot B, prove that A + B = 90 .
5. If sec 4A = cos ec ( A- 20°), where 4A is an acute angle, find the value of A.
6. If A, B and C are interior angles of a D ABC, then show that
B + C A
sin cos .
2 2
=
7. Express sin 67° + cos75° in terms of trigonometric ratios of angles between 0° and 45 .
(Exercise 8.4)
Questions
1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
2. Write the other trigonometric ratios of A in terms of sec A.
3. Evaluate:
(i)
2 2
2 2
sin 63 sin 27
cos 17 cos 73
° + °
° + °
(ii) sin 25°cos65°+ cos 25°sin 65°
4. Choose the correct option. Justify your choice:
(i) 9sec2 A - 9 tan2 A =
(A) 1 (B) 9 (C) 8 (D) 0
(ii) (1+ tanq + secq )(1+ cotq - cos ecq ) =
(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)
2
2
1 tan
1 cot
A
A
+
+
=
(A) sec2 A (B) -1 (C) cot2 A (D) none of these
5. Prove the following identities, where the angles involved are acute angles for which the
expressions are defined:
(i) ( )2 1 cos
cos cot
1 cos
ec
q q q
q
- = -
+
(ii)
cos 1 sin
2sec
1 sin cos
A A
A
A A
+ + =
+
(iii)
tan cot
1 sec cos
1 cot 1 tan
ec
q q q q
q q
+ = +
- -
(iv)
1 sec sin2
sec 1 cos
A A
A A
+ =
-
(v)
cos sin 1
cos cot
cos sin 1
A A
ecA A
A A
- + = +
+ -
, using the identity cos ec2A =1+ cot2 A
(vi)
1 sin
sec tan
1 sin
A
A A
A
+ = +
-
(vii)
3
3
sin 2sin
tan
2cos cos
q q q
q q
- =
-
(viii) ( ) ( ) sin A+ cos ecA 2 + cos A+ sec A 2 = 7 + tan2 A + cot2 A
(ix) ( )( ) 1
cos sin sec cos
tan cot
ecA A A A
A A
- - =
+
(x)
2 2
2
2
1 tan 1 tan
tan
1 cot 1 cot
A A
A
A A
+ - = = + -
No comments:
Post a Comment