Question

cot x sec4x = cot x + 2 tan x + tan3x

Answer 1

Is this equation or identity?

Answer 2

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

Answer 3

\(\cot x \sec^4 x = \cot x + 2 \tan x + \tan^3 x \)

Answer 4

its like above ?

Answer 5

huh?

Answer 6

*the equation u seeing in ur assessment sheet, is it like the one ive posted above ?

Answer 7

its tan cubed x at the end other then that yes

Answer 8

ok thnks :)

pick the side that has more terms, and do SOMETHING and try getting to the other side

Answer 9

here, the right side has more terms, right ?

Answer 10

what? the irght side has more terms yeah

Answer 11

ya so we start with that side, and work, and prove that it equals left side.

Answer 12

okay

Answer 13

\(\cot x + 2\tan x + \tan^3 x\)

\(\frac{1}{\tan x} + 2\tan x + \tan^3 x\)

\(\frac{1+ 2\tan^2 x + \tan^4 x}{\tan x}\)

\(\frac{1+ \tan^2 x + \tan^2x + \tan^4 x}{\tan x}\)

\(\frac{\sec^2 x + \tan^2x + \tan^4 x}{\tan x}\)

\(\frac{\sec^2 x + \tan^2x(1 + \tan^2 x)}{\tan x}\)

\(\frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\)

\(\frac{\sec^2 x(1 + \tan^2x)}{\tan x}\)

\(\frac{\sec^2 x(\sec^2 x)}{\tan x}\)

\(\frac{\sec^4 x}{\tan x}\)

\(\cot x\sec^4 x\)

= LEFT HAND SIDE

Answer 14

thats the complete solution; see if it makes sense

Answer 15

good solve ganeshie.,...........

Answer 16

How did you get rid of the tan^4x? @ganeshie8?

Answer 17

@ganeshie8 i dont understand ur solution

Answer 18

hmm which line ?

Answer 19

the 3rd line from the end.

Answer 20

\[\large \frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\]

Answer 21

you're fine, till this line ?

Answer 22

yes

Answer 23

good, next factor out `sec^2x` from both terms, you get :

\[\large \frac{\sec^2 x(1 + \tan^2x)}{\tan x}\]

Answer 24

still fine ?

Answer 25

oh,ok.so u factored out the sec^2x from the whole numerator?

Answer 26

exactly !

Answer 27

great!thnku very much @ganeshie8

Answer 28

np :)