Question

sinthetha/1+costheta +1+cos theta/sintheta=2cosecthita

Answer 1

hope it Will help you

Answer 2

$\mathsf{\dfrac{sinA}{1+cosA} + \dfrac{1+cosA}{sinA} } \\ \\ \\ \mathsf{ [ \dfrac{sinA}{1+cosA} \times \dfrac{1-cosA}{1-cosA} ] + \dfrac{1+cosA}{sinA} }$



$\mathsf{ \dfrac{ sinA(1-cosA)}{1-cos^{2}A}+ \dfrac{1+cosA}{sinA}}$



$\mathsf{ \dfrac{sinA(1-cosA)}{sin^{2}A} + \dfrac{1+cosA}{sinA}}$



$\mathsf{ \dfrac{1-cosA}{sinA} + \dfrac{1+cosA}{sinA}}$



$\mathsf{\dfrac{1-cosA+1+cosA}{sinA}}$



$\mathsf{\dfrac{2}{sinA}}$



$2 \times \dfrac{1}{sinA}$



2 cosecA




Hence, proved that $\mathsf{\dfrac{sinA}{1+cosA} + \dfrac{1+cosA}{sinA}}$