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sec theta - tan theta = 3 => theta lies in the quadrant

sec theta - tan theta = 3 => theta lies in the quadrant

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Grade:8

1 Answers

Aamina
64 Points
7 years ago
Given that 
sec\Theta-tan\Theta=3 ….............................equation (1)
 
We know that
 
sec2\Theta-tan2\Theta=1
 
From the identity
 
(sec\Theta+tan\Theta)(sec\Theta-tan\Theta)=1
 
So, sec\Theta+tan\Theta=1/3..........................equation (2)
 
On adding equations 1 and 2
 
2sec\Theta=3+1/3
 
2sec\Theta=10/3
 
sec\Theta=5/3
 
Similarly,
 
tan\Theta=4/3
 
as both the values of sec and tan are positive
 
theta is in first quadrant
 
Answer is first option.
 
HOPE THIS HELPS.

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