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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.

Level 3

         

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

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

\[ \implies \large \cos (2A)= \ ? \]

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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