Memorise A B AND C D Formulas In Trigonometry in an Easy Manner

Welcome to this post of learning trigonometric formulas  .Most of the Students or Mathematics Learner ,most of the time confuse to remember or memorise A  B and C  D formulas, They  mixed A B and C D formulas with each other and could not reproduce what they have learnt . So today we going to learn new techniques to learn "How to memorise AB and CD formulas" forever. Before this we must have knowledge of different trigonometric values of different angles in different quadrants.

First of all have a quick look at some of  these formulas

AB Formulas

S N	Fomula	Result
1	sin (A + B)	sin A cos B + cos A sin B
2	sin (A - B)	sin A cos B - cos A sin B
3	cos (A + B)	cos A cos B - sin A sin B
4	cos (A - B)	cos A cos B + sin A sin B

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Tricks to Learn    A  B   Formulae  For  sine  angles

When angles are added  i. e  Sin  ( A+B )  

When Angles are added and then their Trigonometric Ratios is taken , and if we have to take the  Sine of  added angles, then it can be done like this.

Start with  sine of angle A  and multiply it with cosine of  angle B and in other part i. e.  After  +ve sign      Start with Cosine of angle A and multiply with Sine of angle B. i.e. start with sine and ends with sine and in middle both the terms are cosine ,and angles start  A then B again A then again B.

Sin (A+B) = Sin A Cos B + Cos A Sin B

When angles are subtracted    i. e  Sin  ( A-B )  

When Angles are subtracted and  their Trigonometric Ratios is taken , and if we have to take the  Sine of  subtracted  angles, then it can be done like this

    
Start with  sine of angle A  and multiply it with cosine of  angle B and in other part i. e.  After  +ve sign    Start with Cosine of angle A and multiply with Sine of angle B. i.e  start with sine and ends with sine and in middle both the terms are cosine ,and angles start  with A then B again A then again B.

Sin (A - B) = Sin A Cos B - Cos A Sin B

Tricks to Learn    A  B   Formulae For  Cosine  angles

When angles are added   i. e  Cos  ( A+B )  

When Angles are added and then their Trigonometric Ratios is taken , and if we have to take the  Cosine  of  added angles, then it can be done like this.

Start with  cosine of angle A  and multiply it with cosine of  angle B and in other part i. e.  After  -ve sign      Start with Sine of angle A and multiply with Sine of angle B. i.e. 1^st   and 2^nd terms are   cosine and  3^rd and 4^th terms    are sine , Angles start with   A then B again A then again B.

"Here  Sum of cosine of  Two angles  is equal to difference of  product of  cosines of both the angles    and product of sine of both the angles ".

Cos (A+B) = Cos A Cos B - Sin A Sin B

When angles are subtracted    i. e  Cos  ( A-B )  

When Angles are subtracted and  then their Trigonometric Ratios is taken , and if we have to take the  cosine of  subtracted  angles, then it can be done like this.

Cos (A - B) = Cos A Cos B + Sin A Sin B

Start with  cosine of  angle A  and multiply it with cosine of  angle B and in other part i. e.  After  +ve sign      Start with Sine of angle A and multiply with Sine of angle B. i. 1^st   and 2^nd terms are   cosine and  3^rd and 4^th  terms    are sine , and angles start with   A then B again A then again B.

"Here  Difference  of cosine of  Two angles  is equal to the  Sum  of  product of  cosines of both the angles    and product of sine of both the angles" .

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How to Memorise C D Formulae

To learn C D formulae 

Step 1 

Place 2 for all four formulae and  take Trigonometric Ratio of 1st angle for all four formulae which  is (C+D)/2 and again  trigonometric Ratio of  2nd angle which  is (C-D)/2.

Step 2.1 

For addition of Sine Formula start with sine of 1st angle as mentioned in step 1 and multiply it with cos of  2nd angle as mentioned in step 1.

Step 2.2 

For subtraction of Sine Formula start with cosine of 1st angle as mentioned in step 1 and multiply it with sine of  2nd angle as mentioned in step 1.

Step 3.1

For addition of cosine Formula start with cosine of 1st angle as mentioned in step 1 and multiply it with cosine  of  2nd angle as mentioned in step 1.

 

Step 3.2

For subtraction of cosine Formula start with sine of 1st angle as mentioned in step 1 and multiply it with sine   of  2nd angle as mentioned in step 1,and do not forget to multiply it with -ve sign.

or  

If you do not want to multiply it with -ve sign  ,then you can change 2nd angle (D-C)/2 instead of (C-D)/2

CD Formulas

S N	Fomula	Result
1	sin C + sin D	2 sin {(C+D)/2} cos {(C-D)/2}
2	sin C - sin D	2 cos {(C+D)/2} sin {(C-D)/2}
3	cos C + cos D	2 cos {(C+D)/2} cos {(C-D)/2}
4	cos C - cos D	-2 sin {(C+D)/2}  sin {(C-D)/2}
or	cos C - cos D	2 sin {(C+D)/2}   sin {(D-C)/2}

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Conclusion

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How to Memorise A   B and C   D  formulas  easily ,watch this video