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Question (1):
How many radian are there in 120o 30'? Keep the answer correct to three decimal places ( p = 3.1416).
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Answer:
180o = pc
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Question (2):
The wheel of railway carriage is 90 cm in diameter and makes 3 revolutions in a second. How fast is the train moving?
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Answer:
= 30.55 km/hr
1m = 100cm
1km = 1000m
= (1000)(100)
= 100000 cms
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Question (3):
Assuming the mean distance of the earth from the sun to be 149700000 km and the angle subtended by the sun at the eye of a person on the earth is 32'. Find the suns diameter.
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Answer:
Let D be the diameter of the sun in km. The angle subtended by the sun being very small, its diameter is almost equal to an arc of a circle whose centre is the eye of the observer. Also the angle subtended by the sun at the centre of this circle is 32'.
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Question (4):
Prove the following identity:
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Answer:
 
 
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Question (5):
Prove the following identity:
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Answer:
 
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Question (6):
Prove the following identity:
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Answer:
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Question (7):
Prove the following identity:
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Answer:
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Question (8):
Prove the following identity:
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Answer:
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Question (9):
Prove the following identity:
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Answer:
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Question (10):
Prove the following identity:
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Answer:
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Question (11):
Prove the following identity:
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Answer:
 
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Question (12):
Prove the following identity:
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Answer:
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Question (13):
Prove the following identity:
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Answer:
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Question (14):
Prove the following identity:
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Answer:
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Question (15):
Prove the following identity:
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Answer:
 
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Question (16):
Prove the following identity:
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Answer:
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Question (17):
Prove the following identity:
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Answer:
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Question (18):
Prove the following identity:
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Answer:
 
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Question (19):
Prove the following identity:
sec4q(1-sin4q)-2tan2q = 1.
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Answer:
 
 
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Question (20):
Prove the following identity:
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Answer:
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Question (21):
Prove the following identity:
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Answer:
 
 tanq secq - cotq cosecq
 RHS
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Question (22):
Prove the following identity:
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Answer:
 
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Question (23):
Prove the following identity:
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Answer:
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Question (24):
Prove the following identity:
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Answer:
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Question (25):
Prove the following identity:
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Answer:
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Question (26):
Prove the following identity:
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Answer:
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Question (27):
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Answer:
If tan A + sin A = m .... (1)
tan A - sin A = n .... (2)
Adding (1) and (2)
Subtracting (2) from (1)
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Question (28):
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Answer:
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Question (29):
If x sin3q + y cos3q = sin q cos q and x sin q - y cos q = 0.Prove that x2 + y2 = 1.
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Answer:
x sin3q + y cos3q = sin q cos q .... (i)
x sin q - y cos q = 0 .... (ii)
from (i) and (iii)
y = sinq .... (iv)
From (iii) and (iv), x = cos q
\ x2 + y2 = sin2q + cos2q
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Question (30):
If (1-sin A) (1-sin B) (1-sin C)=(1+sin A)(1+sin B) (1+sin C) then, prove that the value of
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Answer:
Let each expression be t then
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