## logynklode 3 years ago cot x sec4x = cot x + 2 tan x + tan3x

1. mahmit2012

Is this equation or identity?

2. logynklode

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

3. ganeshie8

$$\cot x \sec^4 x = \cot x + 2 \tan x + \tan^3 x$$

4. ganeshie8

its like above ?

5. logynklode

huh?

6. ganeshie8

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

7. logynklode

its tan cubed x at the end other then that yes

8. ganeshie8

ok thnks :) pick the side that has more terms, and do SOMETHING and try getting to the other side

9. ganeshie8

here, the right side has more terms, right ?

10. logynklode

what? the irght side has more terms yeah

11. ganeshie8

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

12. logynklode

okay

13. ganeshie8

$$\cot x + 2\tan x + \tan^3 x$$ $$\frac{1}{\tan x} + 2\tan x + \tan^3 x$$ $$\frac{1+ 2\tan^2 x + \tan^4 x}{\tan x}$$ $$\frac{1+ \tan^2 x + \tan^2x + \tan^4 x}{\tan x}$$ $$\frac{\sec^2 x + \tan^2x + \tan^4 x}{\tan x}$$ $$\frac{\sec^2 x + \tan^2x(1 + \tan^2 x)}{\tan x}$$ $$\frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}$$ $$\frac{\sec^2 x(1 + \tan^2x)}{\tan x}$$ $$\frac{\sec^2 x(\sec^2 x)}{\tan x}$$ $$\frac{\sec^4 x}{\tan x}$$ $$\cot x\sec^4 x$$ = LEFT HAND SIDE

14. ganeshie8

thats the complete solution; see if it makes sense

15. jishan

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

16. rubypearl11

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

17. mayaal

@ganeshie8 i dont understand ur solution

18. ganeshie8

hmm which line ?

19. mayaal

the 3rd line from the end.

20. ganeshie8

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

21. ganeshie8

you're fine, till this line ?

22. mayaal

yes

23. ganeshie8

good, next factor out sec^2x from both terms, you get : $\large \frac{\sec^2 x(1 + \tan^2x)}{\tan x}$

24. ganeshie8

still fine ?

25. mayaal

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

26. ganeshie8

exactly !

27. mayaal

great!thnku very much @ganeshie8

28. ganeshie8

np :)

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