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find the maximum of sec x+sec x if x+y=60

find the maximum of sec x+sec x if x+y=60

Grade:10

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
Let
z=secx+secy \Rightarrow \frac{dz}{dx}=secxtanx-secytany
For maxima, we have:
secxtanx=secytany
Thus substituting this in the initial expression gives us:
z=secy+secy\frac{tany}{tanx}=secy\left [ \frac{tanx+tany}{tanx} \right ]=secy\left [\frac{tan\left ( 60-y \right )+tany}{tan\left ( 60-y \right )} \right ]=\frac{sec^{3}y}{\sqrt{3}-tany}Regards
Sumit

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