Prove that: 
tan x/ (secx - 1) - sinx/ (1 + cosx) = 2 cotx

Answer:


Here, we use the simple technique. First we change every terms into sin and cos.
I.e.
Tanx = sinx/ cosx
Secx= 1/ cosx

And then, apply simple mathematics to solve the question as shown in the image above.

You then need to take some terms in common and then cancel the equal terms with opposite signs in the numerator.

Then, you can simply convert the remaining terms into cot. As cotx = cosx/ sinx

So, this is the way how you solve this kind of Trigonometric question and prove the given trigonometric identity in Trigonometry of Mathematics.

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