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subject: Sum And Difference Identities [print this page]

The trigonometric identities are used for relating the angle measures while in some cases they are used for the relation between the sides and the angles of the right angled triangles. The trigonometric identities does not deal with some alone they deal with different angles. And they also involve the operations involving the identities relation for the sum and the difference of the two angle measures. In the following article we will see in detail about the topic sum and difference identities.

More about Sum and Difference Identities :

In these two identities an asymmetry looks like that is not seen in the folder of sums of finitely many terms: in each product, there are only finitely many sine factors and co finitely a lot of cosine factors. If only finitely several types of the terms i are nonzero, then only finitely a lot of the terms on the right side will be nonzero because sine factors will disappear, and in each term, all but finitely many of the cosine factors will be conformity.

Sum identities:

These relations involve the relations involving the trigonometric identities for the sum of two angle values.

'sin(A + B)=sin A *cos B +cos A *sin B'

'cos(A+ B)=cos A *cos B - sin A *sin B'

'tan(A+B) = (tan A + tan B)/(1-tan A *tan B)'

Difference identities :

These relations involve the relations involving the trigonometric identities for the difference of two angle values.

'sin(A - B)=sin A *cosb-cos A* sin B'

'cos(A - B)=cos A *cos B +sin A *sin B'

'tan (A-B) = (tan A - tan B)/(1+tan A*tan B)'

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Example Problems on Sum and Difference Identities:

1. Find the value of 'cos(pi/3 + pi/4)' .

Solution:

'cos(A+B) = cos A*cos B - sin A* sin B'

'cos(pi/3 + pi/4) = cos(pi /4) *cos(pi /3)- sin(pi/4)* sin(pi/3)'

'= (1/ sqrt(2) )(1/2) - (1/sqrt(2))(sqrt(3)/2)'

'=(1-sqrt(3)) / (2sqrt(2))'

2. Solve Sin(30 + 60).

Solution:

The formula for solving sin(30+60) degree is given as,

'Si n(A+B) = Si nA *Cos B +CosA* sin B' .

'sin(30 + 60) = sin30*cos 60 + cos 30*sin 60'

= '1/2 *1/2 + 1/sqrt2 * (sqrt3)/2'

= '1/4 + sqrt3/(2*sqrt2)'

Practice problems on sum and difference identities:

1. Solve 'sin (pi/6 + pi/4)' .

Answer: '(1+sqrt3)/(2*sqrt2)'

2. Solve 'tan (pi/2 + pi/3)' .

Answer: '-2-sqrt3' .

by: nitinp

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