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Sum and Difference Trigonometric Formulas

Sum and Difference Trigonometric Formulas: Level 3 Challenges


cot375+tan375cot75+tan75= ? \large \dfrac{\cot^375^{\circ}+\tan^375^{\circ}}{\cot75^{\circ}+\tan75^{\circ}} = \ ?

sin2(3A)sin2(A)cos2(3A)cos2(A)=2\large \dfrac{\sin^2 (3A)}{\sin^2 (A)}-\dfrac{\cos^2 (3A)}{\cos^2 (A)}=2

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

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

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

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

If we have sin(A+B)cos(AB)=1+515\dfrac { \sin(A+B) }{ \cos(A-B) } =\frac { 1+5 }{ 1-5 } then find the value of tan(π4A)tan(π4B).\tan\left(\dfrac { \pi }{ 4 } -A\right)\tan\left(\dfrac { \pi }{ 4 } -B\right).


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