if cosec theta+cot theta=1/3 find cos theta and determine the quadrant in which theta lies
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Answer:
cosec x + cot x and
cosec x - cot x are reciprocals of each other.
hence, cosec x + cot x = 1/3
cosec x - cot x = 3
Add :
therefore, 2cosec x = 10/3
cosec x = 5/3
sin x = 3/5
identity: sin^2 x + cos^2 x = 1
from here we get,
cos x = 4/5 <= Ans
As the range of theta is not given...
cos x should lie in either 1st or 4th Quadrant since its value is +ve
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