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Show that f(x)=taninverse(sinx+cosx) is strictly increasing on [0;45]

Show that f(x)=taninverse(sinx+cosx) is strictly increasing on [0;45]

Grade:12

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
f ’(x) = (cos x – sin x) / (sinx + cosx)2
 
Now we see that it is strictly increasing in [0 , pi/4] as cos x > sin x in that i terval.
 
hence f(x) is strictly incresig in given interval

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