5 How to prove $2\sin^2(80^\circ) - \sin(70^\circ)=1$? 4 Evaluation of $\lim_{x\rightarrow 0}\frac{\ln(\sin 2x)}{\ln(\sin x)}$ 4 Showing that $\lim_{{x\to 0}}(1+\sin{x})^{\frac{1}{x}} = e$ 3 Integrating $\int\frac{5x^2}{(2+3x^3)^2}\ dx$ 3 If $\frac{\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b}$ show that $a^a \cdot b^b\cdot c^c=1$ .

### Reputation (1,152)

 +10 Integration of $1/(1+\sin 2x)$ +5 Does this trig equation have no solution? $\sqrt 2\sin \left(\sqrt 2x\right)+\sin (x)=0$ -2 Great arc distance between two points on a unit sphere +5 How to prove this complex integration?

### Questions (37)

 10 How to find out the greater number from $15^{1/20}$ and $20^{1/15}$? 5 Does this trig equation have no solution? $\sqrt 2\sin \left(\sqrt 2x\right)+\sin (x)=0$ 3 Which one is greater $\left(5/2\right)^{2/5}$ or $\left(7/2\right)^{2/7}$? 3 What is wrong with the solution? 2 How to prove this complex integration?

### Tags (67)

 29 calculus × 34 5 geometry × 11 14 integration × 13 3 algebra-precalculus × 8 14 limits × 11 3 circles × 5 11 indefinite-integrals × 7 3 logarithms × 3 7 trigonometry × 11 3 limits-without-lhopital × 3