Page 29 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

2
2
Notes Also cos 2A = cos A – sin A
2
= 1 – sin A – sin A
2
2
i.e., cos 2A = 1 – 2sin A

2
Dividing the numerator and denominator of R.H.S. by cos A, we have

(c) To express tan 2A in terms of tan A.

tan 2A = tan(A + A) =

=

Thus we have derived the following formulae :

sin 2A = 2sin A cos A =

2
2
cos 2A = cos A – sin A = 2cos A – 1 = 1 – 2sin A
2
2
tan 2A =

2
cos A = sin A =
2
Example: If verify the following:

(i) 2tan A = 2sin 2A 2sin A cos A =

(ii) cos 2A cos A sin 2A 2cos A 1 1 2sin A =

Solution
(i) sin2A =

2sinAcosA =

=

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