Question

Prove that who wrote one place cause by 1 - cos equal to Cos A + cot

Answer 1

heya mate

AN IDENTITY IS AN EQUALITY that is true for any value of the variable. (An equation is an equality that is true only for certain values of the variable.)

In algebra, for example, we have this identity:

(x + 5)(x − 5) = x2 − 25.

The significance of an identity is that, in calculation, we may replace either member with the other.  We use an identity to give an expression a more convenient form.  In calculus and all its applications, the trigonometric identities are of central importance.

On this page we will present the main identities.  The student will have no better way of practicing algebra than by proving them.  Links to the proofs are below.

Reciprocal identities

sin θ =     1  
csc θ       csc θ =     1  
sin θ cos θ =     1  
sec θ       sec θ =     1  
cos θ tan θ =     1  
cot θ       cot θ =     1  
tan θ

Proof

Again, in calculation we may replace either member of the identity with the other.  And so if we see "sin θ", then we may, if we wish, replace

  it with "   1  
csc θ";  and, symmetrically, if we see  "  1  
csc θ",

then we may replace it with "sin θ".

Problem 1.   What does it mean to say that csc θ is the reciprocal of sin θ ?

To see the answer, pass your mouse over the colored area. 
To cover the answer again, click "Refresh" ("Reload").

It means that their product is 1.

sin θ csc θ= 1.

Lesson 5 of Algebra.

Problem 2.   Evaluate tan 30° csc 30° cot 30°.

tan 30° csc 30° cot30 ° = tan 30° cot 30 ° csc 30 ° = 1· csc 30 ° = 2.

Topic 4.

Tangent and cotangent identities

tan θ  =  sin θ
cos θ        cot θ  =  cos θ
sin θ

Proof

Pythagorean identities

a)  sin2θ + cos2θ  =  1. b)1 + tan2θ  =  sec2θ c)1 + cot2θ  =  csc 2θ a')sin2θ  =  1 − cos2θ.  cos2θ  =  1 − sin2θ.

These are called Pythagorean identities, because, as we will see in their proof, they are the trigonometric version of the Pythagorean theorem.

The two identities labeled a') -- "a-prime" -- are simply different versions of a).  The first shows how we can express sin θ in terms of cos θ; the second shows how we can express cos θ in terms of sin θ.


hope it helps you
(^_^)