Derivatives of Trigonometric functions.
As you know,
The functions SINE x(sin x) , CO-SECANT x(cos x) , TANGENT x(tan x), CO-SECANT x(csc x), SECANT x(sec x) and COTANGENT x(cot x) are called trigonometrical functions.
You can learn more about these functions by searching about it in the search box above.
a> Derivative of sin x:
The derivative of sin x is:
Ley y=SIN x and let this be equation (i)
and let be a small increment in x and be the corresponding small increment in y,
Then we can write:
and let it be equation (ii).
Now if we subtract equation (i) from equation (ii), we can get:
Now using the trigonometrical formula ( sin c – sin d = 2.sin((c-d)/2).cos((c+d)/2)
Now dividing both side of above equation by we get:
b> Derivative of cos x.
The derivative of cos x is:
Let y=cos x
and from trigonometric relations we also know:
Now using chain rule :
c> Derivative of tan x.
The derivative of tan x is:
Now using the quotient rule :
d> Derivative of csc x , secx and cot x.
Using the relation:
csc x= 1/sin x
sec x= 1/cos x
cot x = 1/tan x
and then using the quotient rule, we can find the:
Derivative of csc x:
Derivative of sec x:
Derivative of cot x:
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