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We will learn about the trigonometric ratios of angle A2 in terms of angle A.
How to express sin A, cos A and tan A in terms of A2?
(i) For all values of the angle A we know that, sin 2A = 2 sin A cos A
Now replacing A by A2 in the above relation then we obtain the relation as,
sin A = 2 sin A2 cos A2
(ii) For all values of the angle A we know that, cos 2A = cos2 A – sin2 A
Now replacing A by A2 in the above relation then we obtain the relation as,
cos A = cos2 A2 – sin2 A2
(iii) For all values of the angle A we know that, cos 2A = 2 cos2 A - 1 or 1 + cos 2A = 2 cos2 A
Now replacing A by A2 in the above relation then we obtain the relation as,
cos A = 2 cos2 A2 - 1 or 1 + cos A = 2 cos2 A2
(iv) For all values of the angle A we know that, cos 2A = 1 - 2 sin2 A or 1 - cos 2A = 2 sin2 A
Now replacing A by A2 in the above relation then we obtain the relation as,
cos A = 1 - 2 sin2 A2 or 1 - cos A = 2 sin2 A2
(v) For all values of the angle A we know that, tan 2A = 2 tan A/1 – tan^2 A
Now replacing A by A/2 in the above relation then we obtain the relation as,
tan A = 2tanA21−tan2A2
(vi) For all values of the angle A we know that, sin 2A = 2 tan A/1 + tan^2 A
Now replacing A by A/2 in the above relation then we obtain the relation as,
sin A = 2tanA21+tan2A2
(vii) For all values of the angle A we know that, cos 2A = 1 - tan^2 A /1 + tan^2 A
Now replacing A by A/2 in the above relation then we obtain the relation as,
cos A = 1−tan2A21+tan2A2
Note: Formulas of trigonometric ratios of angle A in terms of angle A2 is also known as sub-multiple angle.
11 and 12 Grade Math
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