A) \[\left( x-\frac{1}{x} \right),x\ne 0\]
B) \[2\left( x-\frac{1}{x} \right),x\ne 0\]
C) \[\left( x+\frac{1}{x} \right),x\ne 0\]
D) \[\frac{1}{2}\left( x+\frac{1}{x} \right),x\ne 0\]
Correct Answer: D
Solution :
(d): \[sec\theta +tan\theta =x\] ?.(i) \[\therefore se{{c}^{2}}\theta -ta{{n}^{2}}\theta =1\] \[\Rightarrow \left( sec\theta +tan\theta \right)\left( sec\theta -tan\theta \right)=1\] \[\Rightarrow sec\theta -tan\theta =\frac{1}{x}\] ?(ii) On adding both the equations \[2sec\theta =x+\frac{1}{x}\] \[\Rightarrow sec\theta =\frac{1}{2}\left( x+\frac{1}{x} \right)\]
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