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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 3 Challenges

$\large \dfrac{\cot^375^{\circ}+\tan^375^{\circ}}{\cot75^{\circ}+\tan75^{\circ}} = \ ?$

$\large \dfrac{\sin^2 (3A)}{\sin^2 (A)}-\dfrac{\cos^2 (3A)}{\cos^2 (A)}=2$

$\implies \large \cos (2A)= \ ?$

In $$\Delta ABC$$, if the length of $$BC$$ is twice the length of $$AC,$$ and $$\angle A-\angle B=90^\circ,$$ what is the value of $$\tan C$$?

$\large \tan(63^\circ) = \sqrt{\sqrt a-\sqrt b} + \sqrt{\sqrt c-\sqrt b}$

The equation above is true for positive integers $$a,b,c$$. What is the value of $$a+b+c$$?

If we have $\dfrac { \sin(A+B) }{ \cos(A-B) } =\frac { 1+5 }{ 1-5 }$ then find the value of $\tan\left(\dfrac { \pi }{ 4 } -A\right)\tan\left(\dfrac { \pi }{ 4 } -B\right).$

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