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Trigonometric Ratios of Angle A2

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 = 2tanA21tan2A2

 

(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 = 1tan2A21+tan2A2

Note: Formulas of trigonometric ratios of angle A in terms of angle A2 is also known as sub-multiple angle.

 Submultiple Angles






11 and 12 Grade Math

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