If sinx=1213 and x∈[0,π], then the value(s) of secx+tanx is/are
A
5
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B
4
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C
−5
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D
−4
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Solution
The correct option is C−5 For sinx=1213
From above triangle
Case 1: when x∈[0,π2] secx=135,tanx=125⇒tanx+secx=5
Case 2: when x∈[π2,π]
in this quadrant secx and tanx both are negative ∴secx=−135,tanx=−125⇒tanx+secx=−5
Alternate:
As we know cos2x+sin2x=1⇒cosx=±√1−sin2x
Now
Case 1: When x lies in 1st quadrant ∴cosx=√1−sin2x
and secx+tanx=1cosx+sinxcosx =1+sinxcosx=1+sinx√1−sin2x=1+1213√1−(1213)2=2513√25169=5
Case 2: When x lies in 2nd quadrant ∴cosx=−√1−sin2x
and secx+tanx=1cosx+sinxcosx =1+sinxcosx=1+sinx−√1−sin2x=1+1213−√1−(1213)2=2513−√25169=−5