Question

1+cosx/sinx + sinx/ 1+cosx = 2/sinx prove it ​

Answer 1

ㅤ$\;\;\underline{\textbf{\textsf{ Given :-}}}$

• ${\sf{ \frac{1 + cosx}{snx} + \frac{sinx}{1 + cosx} = \frac{2}{sinx} }}$

ㅤ$\;\;\underline{\textbf{\textsf{ To Prove :-}}}$

• L.H.S = R.H.S

ㅤ$\;\;\underline{\textbf{\textsf{ Proof :-}}}$

${\sf{ L.H.S = \frac{1 + cosx}{sinx} + \frac{sinx}{1 + cosx} }}$

$= {\sf{ \frac{(1 + cosx)(1 + cosx) + (sinx)(sinx)}{(sinx)(1 + cosx)} }}$

$= {\sf{ \frac{(1 + cosx)^{2} + (sinx)^{2} }{(sinx)(1 + cosx)} }}$

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

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

$= {\sf{ \frac{1 + 1 + 2cosx}{sinx(1 + cosx)} }}$

$= {\sf{ \frac{2 + 2cosx}{sinx(1 + cosx)} }}$

$= {\sf{ \frac{2(1 + cosx)}{sinx(1 + cosx)} }}$

$= {\sf{ \frac{2}{sinx} }}$

$= {\sf{ R.H.S }}$

$\leadsto \ {\boxed{\tt{LHS = RHS}}}$

$\therefore{ \underline{\bf{(Proved)}}}$

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ㅤ$\;\;\underline{\textbf{\textsf{ Need to know :-}}}$

• $\: \: \boxed{\sf{\green{ ( {x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy }} }$

• $\: \: \boxed{\sf{ \green{ {sin}^{2} x + {cos}^{2} x= 1 }} }$

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Answer 2

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