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Subject  >  Math  >  Trigonometry  >  Question and Answers 3

Trigonometry

   
 
Question (1): Prove that (2 cos q + 1) (2 cos q - 1) = 2 cos 2q + 1.
Answer: 



Question (2):
Answer: 

Question (3):
Answer: 


Question (4): Prove that

Answer: 



Question (5):


Answer: 









Question (6):


Answer: 


(i) Dividing (1) by (2) we get














Question (7):
Answer: 












Question (8):


Answer:  Let tan q = t then we have




The above equation is a quadratic in t if t1 = tan a, t2 = tan b are the roots of the equation. Then


Question (9): If the angle q is divided into two parts a and b in such a way
Answer:  By data a + b = q


Dividing (1) by (2), we get






Question (10):
Answer: 








Question (11):
tan (x + y) and tan (x - y).
Answer: 






Question (12):
Answer:  Since x lies in II quadrant, cos x is negative.



Question (13):
Answer: 



Question (14):
Answer: 
Question (15):
Answer: 
Question (16): Prove that tan x = cotx - 2 cot 2x.
Answer: 
[Add and subtract cos2x in the Nr]


Question (17):
Answer: 

Question (18):
Answer: 



Question (19):
Answer: 


Question (20):
Answer: 










By componendo and dividendo, we get




Question (21):
Answer: 
By componendo and dividendo



Question (22):
Answer: 




Question (23):
Answer: 





Question (24):
Answer: 



Question (25):
Answer: 




Question (26):
Answer: 


............................
.......................

Taking the product of two sides and cancelling the factors common to both sides, we get

Question (27):
Answer:  LHS = sin 36o sin 72o sin 108o sin 144o





Question (28):
Answer: 







Question (29):
Answer: 




Question (30): Prove that

Answer: 


Question (31):
Answer: 



Question (32): Prove that 1 + tan 2q tan q = sec 2q.
Answer: 


Question (33): Prove that 1 + cot 2q cot q = cosec 2q cot q.
Answer: 


Question (34): Prove that
cos 4A cos A - sin 4A sin A = cos 3A cos 2A - sin 3A sin 2A.
Answer:  LHS = cos (4A + A) = cos 5A

Question (35):
Answer: 
Question (36):
Answer: 
Question (37):
Answer: 


Question (38): Find tanA when cos 2A = 0.96.
Answer: 
Question (39):
Answer: 
Question (40):
Answer: 





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