How to you simplify cotx + tanx?

We have to evaluate cot x + tan x

Solution

We know that cot x and tan x can be expressed in terms of sin and cos.

\(\cot x=\frac{cos x}{sin x}\) \(\tan x=\frac{sin x}{cos x}\) \(\cot x +\tan x=\frac{cos x}{sin x} + \frac{sin x}{cos x}\)

=\(\frac{\cos ^{2}x +\sin ^{2}x}{\cos x.\sin x}\)

We know the trigonometric identity \({\cos ^{2}x +\sin ^{2}x}=1\)

On substituting in above equation we get

=\(\frac{1}{sinx .cos x}\)

We know that \(\sin 2x=2\sin x\cos x\)

=\(\sin x\cos x=\frac{sin2x}{2}\)

On substituting above value in sin x cos x we get

\(\frac{2}{sin 2x}\)

We know that 1 /sin x = cosec x

\(\frac{2}{sin 2x}\)=\(2\csc (2x)\)

Answer

cot x + tan x= \(2\csc (2x)\)

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