Mister Exam
sin^2a*(1+ctga)+cos^2a*(1+ctga)=sina+cosa; sina+cosa
The solution
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2 2 sin (a)*(1 + cot(a)) + cos (a)*(1 + cot(a)) = sin(a) + cos(a)
$$\left(\cot{\left(a \right)} + 1\right) \sin^{2}{\left(a \right)} + \left(\cot{\left(a \right)} + 1\right) \cos^{2}{\left(a \right)} = \sin{\left(a \right)} + \cos{\left(a \right)}$$
sin(a) + cos(a) = 0
$$\sin{\left(a \right)} + \cos{\left(a \right)} = 0$$
sin(a) + cos(a) = 0
Rapid solution
$$a_{1} = - \frac{\pi}{4}$$
=
$$- \frac{\pi}{4}$$
=
=
$$- \frac{\pi}{4}$$
=
-0.785398163397448
Numerical answer
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a1 = -3.926990816984251
a2 = 2.356194490192345
a3 = -10.21017612416683
a4 = 11.78097245096172
a5 = 5.497787143782138
a6 = -0.7853981633974483
a6 = -0.7853981633974483