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Prove the identity
secx-1/ tan x= tanx/ secx+1
To verify the​ identity, start with the left side and transform it to obtain the right side. Choose the correct step and transform the expression according to the step chosen.
secx-1/ tan x= sec-1 / tanx

Respuesta :

MrRoyal

Answer:

Proved

Step-by-step explanation:

The options are not given. So, I will solve from scratch

Given

[tex]\frac{secx-1}{tan x}= \frac{tanx}{secx+1}[/tex]

Required

Prove

Multiply the right-hand side by [tex]\frac{secx + 1}{secx + 1}[/tex]

[tex]\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}[/tex]

Apply difference of two squares on the numerator

[tex]\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]

In trigonometry:

[tex]tan^2x = sec^2x - 1[/tex]

So, we have:

[tex]\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]

[tex]\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]

tan x cancels out

[tex]\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}[/tex]

Proved

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