Page 31 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

3
2
Notes = 2cos A – cos A – 2cos A(1 – cos A)
3
3
= 2cos A – cos A – 2cos A + 2cos A
3
cos A = 4cos A – 3cosA ....(2)
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(c) tan 3A in terms of tan A
Putting B = 2A in the formula
tan (A + B) =

tan (A + 2A) =

=

=

= …(3)

3
3
(d) Formulae for sin A and cos A
3
Q sin3A = 3sinA – 4sin A
4sin A = 3sinA – sin3A
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or sin A =
3

Thus, we have derived the following formulae:
sin3A = 3sinA – 4sin A
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cos3A = 4cos A – 3cosA
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tan3A =

3
sin A =

3
cos A =

Example 4: If verify that

3
(i) sin3A = 3sinA – 4sin A
(ii) cos3A = 4cos A – 3cosA
3
(iii) tan3A =

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