What are the reciprocal trig identities?

Answer 1

csc (x) = 1 / sin (x)

sec (x) = 1/cos(x)

cot (x) = 1/ tan (x)

Answer 2

The best way to remember this one is to remember the phrase: "Oscar Has A Heap of Apples". The first letter of each word represents the first letter of a triangle side for Sine Cosine and Tangent respectively.
So,
Sine is Opposite over Hypotenuse
Cosine is Adjacent over Hypotenuse
Tangent is Opposite over Adjacent.
The reciprocal of Sine is Cosec or Hypotenuse over Opposite
The reciprocal of Cosine is Secant or Hypotenuse over Adjacent
The reciprocal of Tangent is Cotangent or Adjacent over Opposite
So, Tan = 1 / Cotan and vice verca e.g. Cotan = 1/Tan
The previous concept applies to all reciprocal trig identities

Answer 3

Reciprocal means that if we multiply a function/number with his reciprocal we obtain as result 1
example: a*b=1 so b=1/a

In the case of trig functions, there are defined 6 reciprocal functions, so we have:

senx = 1/cscx like senx=OP/HIP cscx= HIP/OP
secx = 1/cosx
tanx = 1/ctgx
cscx = 1/senx
cosx = 1/secx like cosx = AD/HIP secx= HIP/AD
ctgx = 1/tanx like tanx = OP/AD cotx= AD/OP

so:
senx*cscx = 1
cosx*secx = 1
tanx*cotx = 1

Note that we don't write it sen(^-1)x to say cscx, because this is the notation for inverse trig functions or arcfunctions.

Answer 4

cosecant = 1/sine
secant = 1/cosine
cotangent = 1/tangent

Answer 5

guys i think u got this rong... itz
sin^2(theta)+cos^2(theta)=1

so this will be

co secant^2(theta)+secant^2(theta)=1

similarly

1+tan^2(theta)=secant^2(theta)

this will be

1+cotangent^2(theta)=cos^2(theta)

and

1+cot^2(theta) = cosec^2(theta)


thus

1+tan^2(theta)=sin^2(theta)

BUT THESE ARE NEVER USED!

THIS IS COMPLETELY BOGUS.. SO... ULL HAVE A HARD TIME PROVING THESE..