This presentation is about trigonometric identities and explanation of some identities.

3. A TRIGONOMETRIC IDENTITY is an equation
involving the trigonometric functions that holds for
all values of the variable.

5. sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
By taking L.H.S. :-
sin (a+b) = sin [a-(-b)]
= sin(a) cos(-b) – cos(a) sin(-b)
= sin(a) cos(b) – cos(a) [-sin(b)]
= sin(a) cos(b) + cos(a) sin(b) = R.H.S.
Hence Proved

7. sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
By taking L.H.S. :-

9. By taking L.H.S. :-

12. By taking R.H.S. :-
Multiply by 1 in the form of the conjugate of the
denominator, so we get,
x
x
xx
sin1
cos
sectan
−
=+






+
+
−
=
x
x
x
x
sin1
sin1
sin1
cos

13. Now, by simplifying the numerator and the
denominator, we get,
x
xx
2
sin1
)sin1(cos
−
+
=
x
xxx
2
cos
sincoscos +
=

14. ‘Split’ the fraction and simplify
x
xx
x
x
22
cos
sincos
cos
cos
+=
x
x
x cos
sin
cos
1
+=

15. By using Reciprocal Identities, we get :-
xx tansec +=
And then by using the commutative property of
addition…
xx sectan +=
= L.H.S.
Hence Proved