- #1
tandoorichicken
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How do you do the following integral without using any special methods, i.e., integration by parts, etc.
[tex]\int \frac{\tan x}{\sin x} \,dx[/tex]
?
[tex]\int \frac{\tan x}{\sin x} \,dx[/tex]
?
Integrating tangent (tan) functions can be done by using the substitution method, where you substitute u = tan(x) and then use the trigonometric identity 1 + tan^2(x) = sec^2(x) to simplify the integral.
The formula for integrating sine (sin) over cosine (cos) is to use the substitution method, where you substitute u = cos(x) and then use the trigonometric identity 1 + tan^2(x) = sec^2(x) to simplify the integral.
No, you cannot integrate tangent over sine without using special methods such as substitution or integration by parts. This is because the integral involves a quotient of trigonometric functions, which cannot be solved using basic integration rules.
The easiest way to integrate tangent (tan) multiplied by sine (sin) is to use the product-to-sum identity: tan(x)*sin(x) = (1/2)[sin(2x)/cos(x)]. Then, you can integrate using the substitution method and the trigonometric identity 1 + tan^2(x) = sec^2(x).
There is no specific rule for integrating tangent (tan) multiplied by sine (sin). However, you can use the product-to-sum identity and then solve the integral using the substitution method and trigonometric identities.