Question

prove the trigonometric identities.
sec θ / tan θ = csc θ

Calculation Reason

Answer 1

rewrite sec and tan in terms of sin and cos theta

Answer 2

what's the definition of sec and tan ?

Answer 3

idk

Answer 4

i suck at trig

Answer 5

plz help

Answer 6

cos ,sin ,tan and csc , sec , cot are reciprocal
\[\cos \theta = \frac{1}{\sec \theta} ~~~~~\sin \theta=\frac{1}{\csc \theta} ~~~~\tan \theta =\frac{\sin \theta}{\cos \theta}\]

Answer 7

that's the definition you have to remember that
btw \[\tan \theta = \frac{1}{\cot \theta} =\frac{\sin \theta}{\cos \theta}\]

Answer 8

ok thanks

Answer 9

so how do i solve the question

Answer 10

replace sec theta with 1/cos and tan with sin/cos

Answer 11

i just need three
Calculation Reason

Answer 12

\[\huge\rm \frac{ \sec \theta }{ \tan \theta }=\frac{\frac{1}{\cos \theta}}{\frac{\sin \theta}{\cos \theta}}\]
now simplify

Answer 13

im stuck

Answer 14

\(\color{blue}{\text{Originally Posted by}}\) @Nnesha
cos ,sin ,tan and csc , sec , cot are reciprocal
\[\cos \theta = \frac{1}{\sec \theta} ~~~~~\sin \theta=\frac{1}{\csc \theta} ~~~~\tan \theta =\frac{\sin \theta}{\cos \theta}\]
\(\color{blue}{\text{End of Quote}}\)
these are the trig rules /reciprocal identities

Answer 15

here is an example how to simplify that
`change division to multiplication`
multiply top fraction by the reciprocal of the bottom fraction
\[\large \rm \frac{ \frac{ a }{ b } }{ \frac{ c }{ d } } =\frac{ a }{ b } *\frac{ d }{ c }\]

Answer 16

ok

Answer 17

\[\huge\rm \frac{ \sec \theta }{ \tan \theta }=\frac{\frac{1}{\cos \theta}}{\frac{\sin \theta}{\cos \theta}}\]
try to simplify this by looking at that example let m know what u get

Answer 18

theta=pi/2+2pin

Answer 19

hmm what ?? we don't need exact value
we have to prove that L.H.S = R.H.S
left side is equal to right

Answer 20

\[\huge\rm \frac{\frac{1}{\cos \theta}}{\frac{\sin \theta}{\cos \theta}}\]
how would you change division to multiplication ?

Answer 21

subtract from both sides

Answer 22

we are working on left side
rewrite sec and tan in terms of cos and sin we got this \[\huge\rm \frac{\frac{1}{\cos \theta}}{\frac{\sin \theta}{\cos \theta}}\]
now change division to multiplication
we just working one one side

Answer 23

here is an example
`change division to multiplication`
multiply top fraction by the reciprocal of the bottom fraction
\[\large \rm \frac{ \frac{ a }{ b } }{ \frac{ c }{ d } } =\frac{ a }{ b } *\frac{ d }{ c }\]

Answer 24

0

Answer 25

how did you get 0 show ur steps

Answer 26

multiplied it

Answer 27

what did you multiply ?

Answer 28

a/b*d/c

Answer 29

right now how would you convert this division \[\huge\rm \frac{\frac{1}{\cos \theta}}{\frac{\sin \theta}{\cos \theta}}\]
to multiplication

Answer 30

i suck at trig baby steps plz

Answer 31

nnesha that's my username.
anywayz
forget about sin cos theta
that's same as simple algebra
let cos theta = x
and sin theta = y
so \[\large\rm \frac{ \frac{ 1 }{ x } }{ \frac{ y}{ x} }\]now can you simplify this ?

Answer 32

is this relating to my question

Answer 33

yes

Answer 34

i really dont know

Answer 35

well i don't know what you don't understand