Verifying trigonometric identities

[evolchild9]

verify that each of the following is an identity

cscAsecA=cotA+tanA

sec(squared)y-tan(squared)y=tanycoty

Find a numerical value of one trigonometric function of each x.

2tan x=cot x

tanxcosx=1/2

tanx/sinx={squareroot}2

sinxsecx/cotx=9/16

cosxtanx/cscx=1/9

 

[soroban]

Hello, evolchild9!

I'll assume you know the basic relationships and substitutions.

Find a numerical value of one trigonometric function of each x.

2tan x = cot x

. . . . . . . . . . . .1
2 tan x . = . -------
. . . . . . . . . . tan x

2 tan²x . = . 1

. . . . . . . . . . .1
. . tan²x . = . --
. . . . . . . . . . .2

. . . . . . . . . . . .1
. . tan x . = . --<u>--</u>-
. . . . . . . . . . .√2

(tan x)(cos x) = 1/2

This is the easiest one . . . you can do this yourself, right?

(tan x)/(sin x) = sqrt{2}

. . . . . . . . . . . . . . sin x . . . . . . . . . . . . . .1
The left side is: . -------- .÷ .sin x . = . -------- . = . sec x
. . . . . . . . . . . . . . cos x . . . . . . . . . . . .cos x

Therefore: . sec x .= .sqrt{2}


Could you <u>try</u> the others and show us how far you got?