Løs 1divsin(65-θ)-1divcos(25-θ)

$$1 \div \sin ( 65- \theta ) -1 \div \cos ( 25- \theta )$$

Evaluer

$$\frac{\sin(25)\sin(\theta )+\cos(25)\cos(\theta )-\sin(65-\theta )}{\sin(65-\theta )\left(\sin(25)\sin(\theta )+\cos(25)\cos(\theta )\right)}$$

Differentier w.r.t. θ

$$\frac{\sin(25)\cos(\theta )\left(\cos(65)\sin(\theta )\right)^{2}+\sin(65)\sin(\theta )\left(\cos(25)\cos(\theta )\right)^{2}+\cos(65)\cos(\theta )\left(\sin(25)\sin(\theta )\right)^{2}-\cos(25)\sin(\theta )\left(\sin(65)\cos(\theta )\right)^{2}+\sin(50)\sin(65)\cos(\theta )\left(\sin(\theta )\right)^{2}+\sin(50)\cos(65)\sin(\theta )\left(\cos(\theta )\right)^{2}+\sin(130)\cos(25)\cos(\theta )\left(\sin(\theta )\right)^{2}-\sin(25)\sin(130)\sin(\theta )\left(\cos(\theta )\right)^{2}+\sin(25)\left(\sin(65)\right)^{2}\left(\cos(\theta )\right)^{3}+\sin(65)\left(\sin(25)\right)^{2}\left(\sin(\theta )\right)^{3}+\cos(65)\left(\cos(25)\right)^{2}\left(\cos(\theta )\right)^{3}-\cos(25)\left(\cos(65)\right)^{2}\left(\sin(\theta )\right)^{3}}{\left(\sin(65-\theta )\left(\sin(25)\sin(\theta )+\cos(25)\cos(\theta )\right)\right)^{2}}$$