Question

G = cos^2 45 - 2cos^2 50 + 2sin^2 45 - 2cos^2 40 + 5tan 55.cot 125

Answer 1

\(G=cos^245^0-2\cdot cos^250^0+2\cdot sin^245^0-2\cdot cos^240^0+5\cdot tan25\cdot cot125\)

\(=\left(cos^245^0+2\cdot sin^245^0\right)-2\cdot\left(sin^240^0+cos^240^0\right)+5\cdot tan55\cdot cot\left(180^0-55^0\right)\)

\(=\left(\dfrac{1}{2}+2\cdot\dfrac{1}{2}\right)-2+5\cdot\left(-1\right)\)

\(=\dfrac{1}{2}+1-2-5=\dfrac{1}{2}-6=-\dfrac{11}{2}\)