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Question

Find the value of other five trigonometric ratios:
cosx=12, x lies in third quadrant.

Solution
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cosx=12
secx=1cosx=2
Now sin2x+cos2x=1
sin2x=1cos2xsin2x=114=34sinx=±32
Since x lies in third quadrant, the value of sinx will be negative.
sinx=32
cscx=1sinx=23
tanx=sinxcosx=(32)(12)=3
cotx=1tanx=13

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