NCERT Class 11-Math's: Exemplar Chapter 3 Trigonometric Functions Part 2

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3.1.8 Some formulae regarding compound angles

An angle made up of the sum or differences of two or more angles is called a compound angle. The basic results in this direction are called trigonometric identies as given below:

(i)

(ii)

(iii) v)

(v)

(vi)

(vii)

(viii)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

(xiii)

(xiv)

(xv)

(xvi)

(xvii)

(xviii)

(xix)

(xxi) ) xiii)

xxiii)

xxiii)

Trigonometric functions of an angle of

Let

Therefore, nce,

Hence,

Since,

Also,

Now, we can easily find and as follows:

Hence,