Trigonometry/More About Addition Formulas

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Related Formulae[edit]

Tangent Formulae[edit]

In the last row of expressions, if then the trigonometric functions are all positive so the positive sign is needed before the square root.

Derivations[edit]

Using cofunctions we know that . Use the formula for and cofunctions we can write


Having derived we replace with and use the fact that cosine is even and sine is odd.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle \sin\bigl(a+(-b)\bigr)} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle =\sin(a)\cos(-b)+\cos(a)\sin(-b)}

Related Formulae[edit]

Derivations[edit]

Using and the fact that cosine is even and sine is odd, we have