Question

sinA÷1+cosA+1+cosA÷sinA=2/sinA​

Answer 1

Question :-

Prove that

$\sf{ \frac{ \sin a}{1 + \cos a} + \frac{1 + \cos a}{ \sin a} = \frac{2}{ \sin a} or \: 2 \csc a}$

Formula used :-

$\star \sf{ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy} \\ \\ \star \: { \sin}^{2} \theta + { \cos}^{2} \theta = 1$

Proof :-

Taking left hand side because we need to prove left hand side(LHS) is equal to right hand side (RHS)

$\rightarrow \: \sf{\frac{ \sin a}{1 + \cos a} + \frac{1 + \cos a}{ \sin a} \: } \\ \\ \rightarrow \sf{ \frac{ { \sin}^{2}a + {( 1 + \cos a)}^{2} }{ \sin a(1 + \cos a)} } \\ \\ \rightarrow \sf{ \frac{ { \sin}^{2} a + 1 + { \cos}^{2} a + 2 \cos a}{ \sin a(1 + \cos a)} } \\ \\ \rightarrow \sf{ \frac{1 + 1 + 2 \cos a}{ \sin a(1 + \cos a)} } \: \\ \\ \rightarrow \sf{ \frac{2 + 2 \cos a}{ \sin a(1 + \cos a)} } \\ \\ \rightarrow \sf{\frac{2(1 + \cos a)}{ \sin a(1 + \cos a)} } \\ \: \\ \rightarrow \sf{ \frac{2}{ \sin a} \: \: or \: 2 \csc a}$

LHS = RHS

hence proved .

\_________________/

#answetwithquality

#BAL