Question

if cosec a = 2 , the prove that 1/ tan a + sin a / 1 + cos a =2

Answer 1

Step-by-step explanation:

cosec a = 2

then sin a = 1/2

cos a = √{ 1- cos²x } = √(1-1/4) = √3 /2

tan a = sin a/ cos a = 1/ √3

then,

1/ tan a + sin a / ( 1+ cos a )

= √3 + ( 1/2 ) / (1 + √3/2)

= √3 + 1/ (2+√3)

= (2√3 +3 +1) / (2+√3)

= 2(2+√3) /(2+√3)

= 2 ( proved)