Question

Consider the following statements:
1. If `y=ln(secx+tanx),` then `(dy)/(dx)=secx.`
2. If `y=ln("cosecx-cotx)`, then `(dy)/(dx)="cosec x".`
Which of the above is/are correct?
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer 1

Correct Answer - C
(1)`y=ln(secx+tanx)`
`(dy)/(dx)=(secxtanx sec^(2)x)/(sec x+tanx)`
`=(secx(secx+tanx))/(secx+tanx)=secx`
`y=ln("cosec x"-cot x)`
`(dy)/(dx)=("cosec x"("cosec x"-cotx))/("cosec x"-cotx)="cosec x"`
Hence, both statements are correct.