Question

cos a /1+sin a + 1 +sin a/cos a =2 sec a​

Answer 1

Answer:

LHS =

$= \sf{\dfrac{ cos \sf{a}}{1 + sin \sf{a}} + \: \dfrac{ 1 + sin \sf{a} }{ cos \sf{a} } }$

$= \sf{\dfrac{ cos \sf{a} \: \times cos \sf{a} +(1 + sin \sf{a}) \times (1sin \sf{a}) }{ (1 + sin \sf{a})cos \sf{a} } }$

$= \sf{\dfrac{ {cos}^{2} \sf{a} + (1 + sin \sf{a} {)}^{2} }{ (1 + sin \sf{a}) \times cos \sf{a} } }$

$= \sf{ \dfrac{ {cos}^{2} \sf{a} + ({1}^{2} + {sin}^{2} \sf{a} + 2 \times 1 \times sin \sf{a})}{ cos \sf{a} \times (1 + sin \sf{a}) } }$

$= \sf{\dfrac{( {sin}^{2}\sf{a} + {cos}^{2}) + (1 + 2sin \sf{a})}{ cos \sf{a} \times (1 + sin \sf{a})} }$

$= \sf{\dfrac{1 + 1 + 2 \: sin \sf{a} }{cos \times (1 + sin \sf{a}) } }$

$= \sf{\dfrac{2 + 2sin \sf{a}}{cos \sf{a} \times (1 + sin \sf{a})} = \dfrac{2 \times (1 + sin \sf{a})}{cos \sf{a} \times (1 + sin \sf{a})} }$

$={\sf{\dfrac{2 \times \cancel{(1+sina)}}{cosa \times \cancel{(1+sina)} }}}$

$= \sf{ 2 \times \dfrac{1}{cosa} }$

$= \sf{2 \times sec \sf{a}}$

$= \bf{2sec \sf{a} } \: \: \sf{R.H.S}$

                     

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