and slope of $OP$is $\frac{{\sin \alpha + \sin \beta }}{{\cos \alpha + \cos \beta }} = {m_2}$
.Now ${m_1} \times {m_2} = \frac{{{{\sin }^2}\beta - {{\sin }^2}\alpha }}{{{{\cos }^2}\beta - {{\cos }^2}\alpha }} = - 1$
Hence the lines are perpendicular.
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$f(x) =$ $\left\{ {\begin{array}{*{20}{c}} {\sin \,x}&{if\,\,\,x\,\, \leqslant \,\,c} \\ {ax\, + \,b}&{if\,\,\,x\,\, > \,\,c} \end{array}} \right.$ where $c$ is a known quantity.
If $f$ is derivable at $x = c$ , then the values of $'a'$ $and$ $'b’$ are _____ $and$______ respectively