Consider the following statements: (1) If y=ln(secx+tanx), then dydx=secx (2) If y=ln(cosec xโcotx), then dydx=cosec x, which of the above is/are correct?
A
(1) only
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B
(2) only
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C
Both (1) and (2)
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D
Neither (1) and (2)
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Solution
The correct option is C Both (1) and (2) y=ln(secx+tanx)
Differentiating both the sides, we get
dydx=1secx+tanx⋅(tanxsecx+sec2x)
=secx
y=ln(cosec x−cotx)
Differentiating both the sides, we get
dydx=1cosec x−cotx⋅(−cotxcosec x+ cosec2x)=cosec x
Thus, both statements are correct. Hence, C is correct.