PATHANIA INSTITUTE OF MATHEMATICS
S.C.F 13 PHASE: 2 MOHALI, PH– 98145– 06093
TRIGONOMETRY
M.M.: __________
Date: _________
Three mark questions
4x
2x
grades and another is 3x degrees, while the third is
3
75
radians. Express them all in degrees.
1.
One angle of a triangle is
2.
Sol.
Find in degrees and radians the angle of regular hexagon.
3.
Evaluate: cot 2








sec2 cos  15 sin 2 cos  4 cos cos cos .
4
3
2
2
4
6
4
2
4.
If cot A cot B = 3, show that
5.
Prove that: 2 sin 2
cos(A  B) 1
 .
cos(A  B) 2
3


 2 cos2  2 sec2  10.
4
4
3
Sol.
Five mark questions
6.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in
one second.
7.
Prove that sin 10° sin 50° sin 60° sin 70° =
3 /16.
3
.
2
8.
Prove that cos2 A + cos2 (A + 120°) + cos2 (A - 120°) =
9.
If u n  cos n   sin n . Prove that 2u6 – 3u4 + 1 = 0.
OR
Prove that 2 (cos6  + sin6  ) – 3 (cos4  + sin4  ) + 1 = 0.
10.
Find the value of: tan 142
1o
.
2
Sol.
Three mark questions
1.
Find degree measure of – 2c.
2.
Find in degrees and radians the angles of regular pentagon.
3.
Given sin(A  B) 
3
1
and tan (A  B) 
, find A and B (A, B being positive acute
2
3
angles).
4.
Prove that: 3 cos2

2
 29
 sec
 5 tan 2 
.
4
3
3 2
Sol.
5.
If cot A cot B = 3, show that
cos(A  B) 1
 .
cos(A  B) 2
Five mark questions
6.
Find the angle in degrees through which a pendulum swings if its length is 75 cm and tip
describes an arc of 10 cm.
7.
Prove that:
sec 8A  1 tan 8A

.
sec 4A  1 tan 2A
Sol.
8.
Prove that tan 20º tan 40 º tan 80 º = tan 60 º.
9.
Sol.
Find the value of tan 7
1
.
2
10.
Prove that: tan (B – C) + tan (C – A) + tan (A – B) = tan (B – C) tan (C – A) tan (A – B).
11.
Prove that:
12.
Solve, tan   tan 2  3 tan  tan 2  3.
1
1
1
1



.
cosec   cot  sin  sin  cosec   cot 
11.
If A + B + C = 90o, prove that: sin2 A + sin2 B + sin2 C = 1 – 2 sin A sin B
sin C.
12.
Solve sin x tan x – 1 = tan x – sin x … (i)