TRIGONOMETRIC RATIOS
CLASS X
1.
2.
3.
If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.
If A, B, C, are the interior angles of a triangle ABC, prove that
B
A
CA
 BC
(A) tan 
(B) sin 
  cot
  cos
2
2
 2 
 2 
Prove the following:
cos(90  )sec(90  ) tan 
tan(90  )
(A)

2
cosec(90  )sin(90  ) cot(90  )
cot 
(B)
(C)
4.
tan(90  A) cot A
 cos 2 A  0
2
cosec A
cos(90  A)sin(90  A)
 sin 2 A
tan(90  A)
(D) sin(50  )  cos(40  )  tan1 tan10 tan 20 tan 70 tan80 tan89  1
Evaluate:
2
1
(A)
(cos 4 30  sin 4 45)  3(sin 2 60  sec2 45)  cot 2 30
3
4
2
1
(B) 4(sin 4 30  cos 4 60)  (sin 2 60  cos 2 45)  tan 2 60
3
2
sin 50 cosec 40
(C)

 4cos 50 cosec 40
cos 40 sec50
(D) cosec(65  )  sec(25  )  tan(55  )  cot(35  )
(E)
(F)
2sin 68 2cot15 3tan 45 tan 20 tan 40 tan 50 tan 70


cos 22 5 tan 75
5
3cos 55
4(cos 70 cosec 20)

7sin 35 7(tan 5 tan 25 tan 45 tan 65 tan 85)
sin18
 3 tan10 tan 30 tan 40 tan 50 tan 80
cos 72
cos58 sin 22
cos38 cosec52


(H)
sin 32 cos 68 tan18 tan 35 tan 60 tan 72 tan 55 
If A, B, C are the interior angles of a  ABC, show that:
BC
A
BC
A
 cos
 sin
(A) sin
(B) cos
2
2
2
2
Evaluate each of the following:
(G)
5.
6.
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cos 2 40  cos 2 50
(A) cos(40  )  sin(50  ) 
sin 2 40  sin 2 50
cos 70
cos 55 cosec35
(B)

sin 20 tan 5 tan 25 tan 45 tan 65 tan 85
 cos 58 
 cos 38 cosec 52 
(C) 2 
 3

 sin 32 
 tan15 tan 60 tan 75 
7.
8.
9.
10.
tan A tan B  tan A cot B sin 2 B

 tan A
sin A sec B
cos 2 A
If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
1
1
tan A  tan B
If A and B are acute angles such that tan A  , tan B  and tan(A  B) 
, show
3
2
1  tan A tan B
that A + B = 45°.
Without suing trigonometric tables, evaluate the following:
3cos 55
4(cos 70 cosec 20)
(A)

7sin 35 7(tan 5 tan 25 tan 45 tan 65 tan 85)
If A + B = 90°, prove that
(B)
 tan .cot(90  )  sec  cosec(90  )  sin 2 35  sin 2 55
tan10 tan 20 tan 30 tan 70 tan 80
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