Question

Verify the identity. Show your work.

cot θ ∙ sec θ = csc θ

Answer 1

thats my work :


secx -1 / tanx
(1/cosx -1)/ tanx
(1/cosx - cosx/cosx)/(sinx/cosx)
(1 - cosx / cosx) / (sinx/cosx)
(1 - cosx) / sinx
For the other side (right), Step B:

(sinx/cosx) / (1/cosx +1)
(sinx/cosx) / (1/cosx + cosx/cosx)
(sinx/cosx) / (1+cosx / cosx)
sinx / (1+cosx)



Step C (left side)

(1 - cosx) / sinx
(1-cosx)sinx / sin^2x
(1-cosx)sinx / (1-cos^2x) pythagorean property (sin^2x + cos^2x = 1)
(1-cosx)sinx / (1+cosx)(1-cosx) factor the bottom
(sinx / (1+cosx) Cancel the common (1-cosx)

secx-1 / tanx = sinx / (1+cosx)

Step A
Step C
backwards of Step B
but my teacher said :
To prove an identity you are required to show that the LHS
of the relationship given is = the RHS. It is different to solving an equation.
You cannot take terms across the = and you cannot multiply or divide both sides by anything.
You do so by using accepted identities that enable you to rewrite one or both sides so that they
are exactly the same i am confused now what i did wrong please help

Answer 2

|@ganeshie8 @ParthKohli @mathstudent55 @mathmath333

Answer 3

@eliassaab @ganeshie8

Answer 4

That's way too much work for this problem!

Answer 5

then? O_0?

Answer 6

Why not just write all the terms of the LHS in terms of sin and cos?

Answer 7

i am very bad at calculus and it took me hours to get it these questions are those i got wrong in test :(

Answer 8

plzz show me ur work so i can get it

Answer 9

its not that hard like parth said
just change cot theta
okay so here are identities that we need
we have to prove right that both side equal ??