8/11/2019 Trigo Viii & Ix
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Exercise-1
1 If17
8cos = , find the other five trigonometric ratios.
2 Given5
12tan = , calculate sin , cos and verify that 1cossin
22=+
3 In ABC, right angled at C, if3
1tan =A , show that 1sincoscossin =+ BABA .
4 ABC has a right angle at A. In each of the following, find sin
B, cos C and tan B
(a) AB = AC = 1 cm
(b) AB = 5 cm, BC = 13 cm
(c) AB = 20 cm, AC = 21 cm
5 Given29
21cos = , determine the value of
sintan
sec
.
6 If 2cos =ecA , find the value ofA
AA
cos1
sincot
++ .
7 If2
1sin =B , show that 0cos4cos3
3= BB .
8 If5
12cot =B , show that BBBB
2222tansinsintan = .
9 If
3
4tan = , find the value of
cos2sin3
cos2sin3
+.
[ Hint: Divide the numerator and denominator by cos ]
10 Verify : cos 60 cos 30 - sin 60 sin 30 = cos 90
11 If ( ) 1sin =+ BA and ( )2
3cos = BA , 0 < A + B 90 and A > B, find A and B.
12 Evaluate :
(a) cos 30 cos 45 - sin 30 sin 45
(b) tan260 + 4 cos
245 + 3 sec
230 + 5 cos
290
(b)
+
60cos60sec
60tan
ec
13 Show that:
(a)2
360sin30sin45sin 222 =++ (b)
4
360cos60sin2 2 =
14 Given A = 30, verify
(a) AAA cos3cos43cos 3 = (b)A
A2tan1
1cos
+
=
15 Verify each of the following
(a) 145cos245sin2190cos 22 == (b) =+
30tan
30tan60tan1
30tan60tan
8/11/2019 Trigo Viii & Ix
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Exercise-2
1 If 2cos =ecA , find the value ofA
A
A cos1
sin
tan
1
++ .
2 Verify that:
(i)2
3
30tan1
30tan260sin
2 =+
= (ii)
2
130sin30cos60cos 22 ==
3 ABC is a right triangle, right angled at C. If A = 30 and AB =
40units find the remaining
two sides and B of ABC .
4 If 3cot2 = , the value of+
cos5sin3
sin2cos5is
(i)11
24 (ii)
18
13 (iii)
19
11 (iv)
21
11
5 Ifb
a=tan , then the value of
+
+
2
2
sec1
2cosecis:
(i)
( )
( )222
222
2
3
bab
baa
+
+
(ii)
( )
( )222
222 2
bab
baa
+
+
(iii)
( )
( )222
222
2
3
baa
bab
+
+
(iv)
( )
( )222
222 2
baa
bab
+
+
6 Prove that: =
++
+
eccos2
1sec
1sec
1sec
1sec
7 Prove that: ( ) ( ) ( ) ( ) 222244 cos211sin2cossincossin
===
8 Prove that: ( )( )( ) 1cottancossecsincos =+ ec
9 Prove that: ( )( ) 1tansecsin1sec =+
10 Prove that:1sin2
2
cossin
2
cossin
cossin
cossin
cossin222
=
=
+
+
+
AAAAA
AA
AA
AA.
11 Prove that: (i) =
++
+
eccos2
sin
cos1
cos1
sin (ii)
tansec
tansec
1+=
12 If 900 and 1sectan3 = , than has the value
(i) 30 (ii) 45 (iii) 60 (iv) 90
