Basic Trigometric Identities?

Start with replacing tan x = sin x / cos x
cos x + sin²x / cos x

Now get a common denominator of cos x:
cos²x / cos x + sin²x / cos x

Combine the fractions:
(cos²x + sin²x) / cos x

We know by trig. identities that the numerator is now 1:
1 / cos x

And this is the same as sec x.

Therefore:
cos x + sin x tan x = sec x

Hi there its all very simple
trignometry is nothing but science of measurement of triangles.=)
Sine (sin)refers to the Perpendicular/Hypertenouse of triangle
Cosine(cos)refers to the Base/Hypertenouse
Tangent(tan)refers to the Perpendicular/Base
Cotangent(cot)refers to the Base/perpendicular
Secant(sec)refers to the Hypertenouse/Base
Cosecant(cosec)refers to the Hypertenouse/Perpendicular

U c tht most of them are related to one another
For example -
tan X=sin X/cosX

because-
sin X=perpendicular/hypertenouse
And
cos X=base/hypertenouse
If we divide the sin X and cos X,the hypertenouse will be cancelled and we will have perpendicular/Base,which is nothing but tan X!

Similarly most equations of trignometry can be equated to other equations which are equal!
We just have to prove it...
by simplifying 1 equation first and try to c tht it is equivalent to the other

Hope it helped =P

cos x + sin x tan x = sec x
cosx +sinx*sinx/cosx = 1/cosx
Now multiply by cosx, getting:
cos^2x + sin^2x = 1
1 = 1

cos x + sin x tan x = sec x

cos x + sin x (sin x/cos x) = sec x

(cos² x + sin² x)/cos x = sec x

Since
cos² x + sin² x = 1

1/cos x = sec x

sec x = sec x
.

cos x + sin x tan x = cos x + sin x*sin x/cos x
cos x + sin x*sin x/cos x = cos x + sin^2 x/cos x
Now combine fractions
cos x = cos^2 x/cos x
cos x + sin^2 x/cos x = (cos^2 x + sin^2 x)/cos x
But we know (cos^2 x + sin^2 x) = 1, so
(cos^2 x + sin^2 x)/cos x = 1/cos x, which is sec x.

now on, sinx = s, cosx = c , tanx = t, secx = e

c+st = c+s(s/c) = (c^2 + s^2 )/c = 1 / c = e

tan x = sin x / cos x
cos x + sin x tan x = cos x + sin x * sin x / cos x
= cos² x / cos x + sin² x / cos x
= (cos² x + sin² x) / cos x
= 1 / cos x (use cos² x + sin² x = 1)
= sec x