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Question

Consider the following statements:
(1) If y=ln(secx+tanx), then dydx=secx
(2) If y=ln(cosec xcotx), 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 xcotx)
Differentiating both the sides, we get
dydx=1cosec xcotx(cotxcosec x+ cosec2x)=cosec x
Thus, both statements are correct.
Hence, C is correct.

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