Question

Given coto=7/8
then evaluate
(i)
(1 + sin 0) (1 - sin )/
(1 + cos 0) (1 -cos)

ii)
(1+sin)/
coso​

Answer 1

Answer:

Step-by-step explanation:

$cot A = \frac{7}{8}\\1 + cot^2A = cosec^2A\\1 + (\frac{7}{8})^2 = cosec^2A\\1 + \frac{49}{64} = cosec^2A\\cosec^2A = \frac{113}{64}\\cosecA=\sqrt{\frac{113}{64}}=\frac{\sqrt{113}}{8}\\sin A = \frac{1}{cosecA} = \frac{8}{\sqrt{113}}\\cos A = \sqrt{1-sin^2A}=\sqrt{1-\frac{64}{113}}=\sqrt{\frac{49}{113}}=\frac{7}{\sqrt{113}}$

$1) \frac{(1+sinA)(1 - sinA)}{(1+cosA)(1-cosA)}\\=\frac{1-sin^2A}{1-cos^2A}\\=\frac{cos^2A}{sin^2A}\\=\frac{\frac{49}{113}}{\frac{64}{113}}=\frac{49}{64}\\2) \frac{1+sinA}{cosA}\\=\frac{1+ \frac{8}{\sqrt{113}}}{\frac{7}{\sqrt{113}}}\\=\frac{\sqrt{113}+8}{7}$