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Question

# Consider the following statements:(1) If y=ln(secx+tanx), then dydx=secx(2) If y=ln(cosec xโcotx), 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 getdydx=1secx+tanx⋅(tanxsecx+sec2x) =secx y=ln(cosec x−cotx) Differentiating both the sides, we getdydx=1cosec x−cotx⋅(−cotxcosec x+ cosec2x)=cosec xThus, both statements are correct.Hence, C is correct.

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