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Sum and Difference Trigonometric Formulas

These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.

Sum and Difference Trigonometric Formulas: Level 2 Challenges


If \(\sin\theta= \cos\theta\), find the value of \(\cos 2\theta\).

If \(A + B = 225^{\circ}\), find \((1+\tan A)(1+\tan B),\) where defined.

\[\large \frac {1}{\cos 80^\circ } - \frac {\sqrt 3}{\sin 80^\circ } = \ ? \]

Hint: How can we write the numerators in relation to common trig values?

If \[\cos\left[6\arccos \left(\dfrac{1}{3}\right)\right] = \frac{A}{B},\] where \(A\) and \(B\) are relatively prime positive integers, find \(B-A.\)

\[ \sin^2 18^ \circ + \sin ^2 30 ^ \circ. \]

Which of the following is equal to the above expression?


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