[tex]\sqrt{\frac{1+sin\alpha}{1-sin\alpha}}+\sqrt{\frac{1-sin\alpha}{1+sin\alpha}}=\\\\\sqrt{\frac{1+sin\alpha}{1-sin\alpha}\cdot\frac{1+sin\alpha}{1+sin\alpha}}+\sqrt{\frac{1-sin\alpha}{1+sin\alpha}\cdot\frac{1-sin\alpha}{1-sin\alpha}}=\\\\\sqrt{\frac{(1+sin\alpha)^2}{1-sin^2\alpha}}+\sqrt{\frac{(1-sin\alpha)^2}{1-sin^2\alpha}}}=\\\\\sqrt{\frac{(1+sin\alpha)^2}{cos^2\alpha}}+\sqrt{\frac{(1-sin\alpha)^2}{cos^2\alpha}}}=[/tex]
[tex]\frac{(1+sin\alpha)}{cos\alpha}}+\frac{(1-sin\alpha)}{cos\alpha}}}=\\\\\frac{1+sin\alpha+1-sin\alpha}{cos\alpha}}}=\frac{2}{cos\alpha}[/tex]
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
[tex]\sqrt{\frac{1+sin\alpha}{1-sin\alpha}}+\sqrt{\frac{1-sin\alpha}{1+sin\alpha}}=\\\\\sqrt{\frac{1+sin\alpha}{1-sin\alpha}\cdot\frac{1+sin\alpha}{1+sin\alpha}}+\sqrt{\frac{1-sin\alpha}{1+sin\alpha}\cdot\frac{1-sin\alpha}{1-sin\alpha}}=\\\\\sqrt{\frac{(1+sin\alpha)^2}{1-sin^2\alpha}}+\sqrt{\frac{(1-sin\alpha)^2}{1-sin^2\alpha}}}=\\\\\sqrt{\frac{(1+sin\alpha)^2}{cos^2\alpha}}+\sqrt{\frac{(1-sin\alpha)^2}{cos^2\alpha}}}=[/tex]
[tex]\frac{(1+sin\alpha)}{cos\alpha}}+\frac{(1-sin\alpha)}{cos\alpha}}}=\\\\\frac{1+sin\alpha+1-sin\alpha}{cos\alpha}}}=\frac{2}{cos\alpha}[/tex]