Mathematics: Sec^6x(secxtanx)-sec^4(secxtanx)=sec^5xtan^3x verify the trigonometric identity

Sec^6x(secxtanx)-sec^4(secxtanx)=sec^5xtan^3x verify

gabedafame26

09.01.2022

I guess you mean

$\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan^3x$

On the left side, we have a common factor of $\sec^4x(\sec x\tan x)=\sec^5x\tan x$ , so that

$\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan x(\sec^2x-1)$

Recall that

$\sec^2x=1+\tan^2x$

from which it follows that

$\sec^5x\tan x(\sec^2x-1)=\sec^5x\tan x\tan^2x=\sec^5x\tan^3x$

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Cleotilde14151

11.09.2020

Answer and explanation:

Given : $f(x)=y=\frac{3x}{8+x}$

To find : Arrange the equations in the correct sequence to find the inverse of f(x) ?

Solution :

Writing step by step to find inverse,

Step 1 - Interchange y with x,

$x=\frac{3y}{8+y}$

Step 2 - Cross multiply,

x(8+y)=3y

Step 3 - Apply distributive property,

8x+xy=3y

Step 4 - Take y term one side,

8x=3y-xy

Step - 5 Take y common,

8x=y(3-x)

Step 6 - Take x term together,

$y=\frac{8x}{3-x}$

or $y=f^{-1}(x)=\frac{8x}{3-x}$

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