A trigonometric problem

Geometry Level 4

If tan⁡A\tan A and tan⁡B\tan B are the roots of x2−12x+32=0x^2 - 12x + 32 = 0.

What is the value of

sin⁡2(A+B)−12sin⁡(A+B)cos⁡(A+B)+32cos⁡2(A+B)? \sin^2(A+B)- 12\sin(A+B)\cos(A+B) + 32\cos^2(A+B) ?

Vijay Simha by Vijay Simha
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