Question

Integrate the function

$\huge\green\tt\frac{ \sqrt{tanx} }{sinxcosx}$

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Answer 1

Answer:

The answer is

=2√tanx+C

Explanation:

We need

tanx = sinx/cos

xtanx=tanxsecx

Therefore, the integral is

I=∫√tanxd

xsinxcosx=∫√

tanxdxtanxsecx⋅1secx

=∫sec 2xdx√tanx

Let

u=tanx ,

⇒, du=sec2xdx

The integral is

I=∫(du)√u

=√u12

=2√u

=2√tanx+C

Step-by-step explanation:

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Answer 2

Given

$\sf\frac{ \sqrt{tan\:x} }{sin\:x\:cos\:x}$

We Doing

• Simplify the Equation

Solution

Your Solution in the above picture !

Some Basics about our question

☞ Sin is equal to the side opposite the angle that you are conducting the functions on over the hypotenuse which is the longest side in the triangle.

☞ Cos is adjacent over hypotenuse.

☞ Tan is opposite over adjacent, which means tan is sin/cos. this can be proved with some basic algebra.