Explanation First write the all formulas of sum and differences of sine, cosine, and tangent as sin ( α + β ) = sin α cos β + cos α sin β sin ( α − β ) = sin α cos β − cos α sin β cos ( α + β ) = cos α cos β − sin α sin β cos ( α − β ) = cos α cos β + sin α sin β And, tan ( α + β ) = tan α + tan β 1 − tan α tan β tan ( α − β ) = tan α − tan β 1 + tan α tan β The way to make the formula sin ( α + β ) = sin α cos β + cos α sin β is easy to remember as 1. In case of sine function when there is positive sign between angle, that is, sin ( α + β ) , then expansion of this also contains positive sign as sin α cos β + cos α sin β . 2. The other way to make it easy to remember is write sine as an angle of α and cosine as an angle of β and multiply them and put positive sign as discussed above. Now for second term, reverse the first term, that is, write cosine as an angle of α and sine as an angle of β and multiply them. So, the formula becomes sin ( α + β ) = sin α cos β + cos α sin β The way to make the formula sin ( α − β ) = sin α cos β − cos α sin β is easy to remember as 1. In case of sine function when there is negative sign between angle, that is, sin ( α − β ) , then expansion of this also contains negative sign as sin α cos β − cos α sin β . 2. The other way to make it easy to remember is write sine as an angle of α and cosine as an angle of β and multiply them and put negative sign as discussed above. Now for second term, reverse the first term, that is, write cosine as an angle of α and sine as an angle of β and multiply them. So, the formula becomes sin ( α − β ) = sin α cos β − cos α sin β The way to make the formula cos ( α + β ) = cos α cos β − sin α sin β is easy to remember as 1. In case of cosine function when there is positive sign between angle, that is, cos ( α + β ) , then expansion of this contains negative sign as cos α cos β − sin α sin β . 2. The other way to make it easy to remember is write cosine as an angle of α and cosine as an angle of β and multiply them and put negative sign as discussed above. Now for second term, write sine as an angle of α and sine as an angle of β and multiply them. So, the formula becomes cos ( α + β ) = cos α cos β − sin α sin β The way to make the formula cos ( α − β ) = cos α cos β + sin α sin β is easy to remember as 1. In case of cosine function when there is negative sign between angle, that is, cos ( α − β ) , then expansion of this contains positive sign as cos α cos β + sin α sin β . 2. The other way to make it easy to remember is write cosine as an angle of α and cosine as an angle of β and multiply them and put positive sign as discussed above. Now for second term, write sine as an angle of α and sine as an angle of β and multiply them. So, the formula becomes cos ( α − β ) = cos α cos β + sin α sin β The way to make the formula tan ( α + β ) = tan α + tan β 1 − tan α tan β is easy to remember as 1. It is known that tan θ = sin θ cos θ

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ISBN: 9781323142707

Author: Blitzer

Publisher: Pearson Custom Publishing

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Chapter 6.2, Problem 106E

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The way to make the formula for sum and differences of sine, cosine, and tangent easier to remember.

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Chapter 6.2, Problem 105E

Chapter 6.2, Problem 107E

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