Question

prove that ½{sinA/1+cosA + 1+cosA/sinA}=1/sinA​

Answer 1

$1 \div 2( \sin(a) \div 1 + \cos(a) + 1 + \cos(a) \div \sin(a)) \\ 1 \div 2( \sin {a}^{2} ) +(1 + \cos(a) )^{2} \div \sin(a)( \cos(a) ) \\1 \div 2 \sin( {a}^{2} ) + \cos( {a}^{2} ) + 1 + 2 \cos(a) \div \sin(a) ( \cos(a) + 1) \\1 \div 2 2(1 + \cos(a) \div \sin(a) ( \cos(a) + 1) \\ 1 \div 2 \times 2 \div \sin(a) \\ 1 \div \sin(a) \\ hence \: proved$

this is the answer frnds

Answer 2

Answer:

$\frac{1}{2} ( \frac{ \sin(x) }{1 + \cos(x) } + \frac{1 + \cos(x) }{ \sin(x) } ) \\ \frac{1}{2} \frac{ { \sinx}^{2} + {1 + \cos(x) }^{2} }{ \sin(x)(1 + \cos(x) )} \\ \frac{ { \sin(x) }^{2} + 1 + { \cos(x) }^{2} + 2 \cos(x) }{ \sin(x) (1 + \cos(x) )} \\ \frac{1 + 1 + 2 \cos(x) }{ \sin(x) (1 + \cos(x) } \\ \frac{1}{2} ( \frac{2 + 2 \cos(x) }{ \sin(x)(1 + \cos(x))} = \frac{2}{ \sin(x) }$

Hope its help uh❤