32 



therefore 



therefore 

 therefore 



COTANGENT. SECANT. 



Ay = tan (x + h) tan x 



_ sin (x + h} sin a; 

 cos (x + h) cos x 



sin (x -f h x) _ sin h 



cos (x + h) cos x cos (a; + h) cos a; ' 



Ay _ sin ^ 1 



A# ~ h cos (a; + h) cos a? * 



dx cos 2 a; " 



54. Differential coefficient of cot x. 

 By proceeding as in the last Example, we find that if 

 y = cot ac, 

 dy _ 1 



dx 



sin x 



55. Differential coefficient of sec #. 

 Let y = seca:, therefore 



y + Ay = sec (x + h}, 

 therefore Ay = sec (x + Ji) sec x 



1 1 cos x cos (x + h} 



cos arcos (x + h) ' 



therefore - = 



. h 

 sin - 



cos x cos (x + h} h 

 2 



f dy sin x 



therefore - T - = r . 

 cue cos x 



