If x is in third quadrant,then (a).Choose the possible value of cosec x from the bracket[-3/5,3/5,5/3,-5/3] (b).Evaluate tanx-secx for the x in the part (a)?
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Answers
Given : x is in third quadrant
To Find : possible value of cosec x
-3/5, 3/5, 5/3, -5/3
Evaluate tanx-secx
Solution:
x is in third Quadrant
Cosec is - ve in 3rd and 4th while +ve in 1st and 2nd Quadrant
Hence Cosecx will be - ve
Cosecx range is (-∞ , - 1) ∪ ( 1 , ∞ )
and Cosecx is -ve in third Quadrant
Hence cosecx will lie in (-∞ , - 1)
- 5/3 is the only option Which satisfy this
cosecx = - 5/3
cosec²x = 1 + cot²x
=> (-5/3)² = 1 + tan²x
=> cotx = +/-4/3
cotx is + ve in 3rd Quadrant
Hence tanx = 1/cotx = 3/4
sec²x = 1 + tan²x = 1 + (3/4)² = 5/4
Secx = - 5/4 as secx is -ve in 3rd Quadrant
tanx-secx = 3/4 - (-5/4)
= 8/4
= 2
tanx-secx = 2
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