# Connect the curve 6

Algebra Level 4

We plot two continuous curves $f\left( x \right) =\sin { \left( x+a \right) } \cos { \left( x-a \right) } \\ g\left( x \right) =\sin { \left( x-a \right) } \cos { \left( x+a \right) }$

And another curve $h\left( x \right) =\frac { f\left( x \right) }{ g\left( x \right) }$

It is observed that for some $$a$$, such that $$\frac { \pi }{ 2 } <a<\pi$$, the curve of $$h\left( x \right)$$ is tangent to the curve of $$f\left( x \right)$$ at point $$\left( t,h\left( t \right) \right)$$. Here, $$0<t<\frac { \pi }{ 2 }$$.

If $$t+a$$ can be expressed as $\frac { A }{ B } { \pi }^{ C }+D$ such that $$gcd\left( A,B \right) =1$$ and $$A,B,C,D\in Z$$ , find the value of $AB+C+D$

Hint: Differentiate

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