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B
f(x)=tanx
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C
g(x)=2x
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D
g(x)=x
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Solution
The correct options are Cf(x)=tanx Dg(x)=x Given ∫sinxd(secx)=f(x)−g(x)+c ...(1) Consider, ∫sinxd(secx)=∫sinxd(secx)dxdx=∫sinxsecxtanxdx =∫tan2xdx =∫(sec2x−1)dx =tanx−x+C So, by (1), we get ∴f(x)=tanx,g(x)=x