[Math] Find the value of: sin(100) + sin(125) + sin(100)•sin(125)

trigonometry

This question has been troubling me since last few days. Can anyone pls solve without a calculator? Thanks in advance.
All values are in degrees.
Also, the question has the following options:
0,0.5,-1,1,2

Ps: the question asked to solve all the problems which were possible to solve without a calculator and this is a part of it. I don't know whether it is possible to solve this without a calculator.
Here the second part of the question: Find the value of: tan(100) + tan(125) + tan(100)•tan(125)

Best Answer

Still incorrect problem. Without a calculator you know that both $\sin$ values are in the interval $(\frac{\sqrt{2}}{2},1)$, so the expression is at least $2\frac{\sqrt{2}}{2} + (\frac{\sqrt{2}}{2})^2 \approx 1.4 + 0.5 = 1.9\dots$. Therefore the best guess option would be 2. But this far away from the true value $2.610667\dots$

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