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    trigonometry transformation formulas

    Deepika 24th Mar, 2020
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    Answer (1)
    Sai Sri Nandan Ch 24th Mar, 2020

    Hello,

    There are 8 Trigonometric Transformation Formulas. The beauty of these formulas is that addition of two trigonometric ratios can be converted into multiplication and vice versa. This will help to cancel terms from numerator and denominator or will let you split the numerator into two different fractions.

    2 \sin A \cos B = \sin (A + B) + \sin (A - B) \\ \\ 2 \cos A \sin B = \sin (A + B) - \sin (A - B) \\ \\ 2 \cos A \cos B = \cos (A + B) + \cos (A - B) \\ \\ 2 \sin A \sin B = \cos (A - B) - \cos (A + B)

    By replacing A+B as C and A-B as D, we can rewrite the formulas in another fashion:

    \sin C + \sin D = 2 \sin \frac{1}{2}( C + D) \cos \frac{1}{2}( C - D) \\ \\ \sin C - \sin D = 2 \sin \frac{1}{2}( C - D) \cos \frac{1}{2}( C + D) \\ \\ \cos C + \cos D = 2 \cos \frac{1}{2}( C + D) \cos \frac{1}{2}( C - D) \\ \\ \cos D - \cos C = 2 \sin \frac{1}{2}( C + D) \sin \frac{1}{2}( C - D)

    Hope this helps.

    Thanks.

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