No. 39.
1. Define a radian.
(1.)
675
TRIGONOMETRY.
SENIOR.
Find the radian measure of :-
a right angle;
(2.) the exterior angle of a regular octagon.
2. Prove the following identities :-
(1.) (lan B + see B)
(2.) cos (2A-3B)+cos 3B
sin (2A-3B) + sin 3B
1
+ sin B
-
1
sin B
=cot A
B
0
A
(3.)
tan- tan
+ tan
tan
2
A
B
+ tan
tan
= 1
2
2
if A + B
C
180°
3. The angle of elevation of the top of a pillar is 30° and on approaching 20 feet nearer it is 60°; find the height of the pillar.
4. Show how to solve a triangle having given 3 sides.
If the sides of a triangle are as 4:7: 5, find the greatest
angle, given cos 78°—27′ =}.
5. Find the radius of a circle circumscribing a triangle.
Prove that in any triangle:-
a cos A + b cos B + e cos C 4R sin A sin B sin C.
No. 40.
TRIGONOMETRY.
JUNIOR.
1. Prove geometrically the following identities:-
(1) cos 2 A + sin 2 A = 1.
(2) cosec
2 A
I + cot? A.
1
(3) tan 30°
2. Define a radian. Find the radian measure of a right angle.
Find the numerical value of :-
2 sin 11 + 1⁄2 cos 꽃
4
3. If cot A=c, show that c+c ̄1=sec A cosec A.
4. The angle of elevation of the top of a tower is 30°, on walking 100 yards nearer the elevation is found to be 60°. Find the height of the tower.
5. Prove the formula :-
sin (A + B) = sin A cos B-c
Prove the identities:-
--cos A sin B.
cos (A-B)
cos A sin B
Cot B+tan A.
tan (45° + A):
1 + tan A tan A