Question

Cot theta + cosec theta = root 3 , solve for theta

Answer 1

Hi ,

According to the problem given,

CosecX + CotX = √3 -----( 1 )

We know that ,

Cosec² X - Cot² X = 1

( CosecX + Cot X )(CosecX - CotX) =1

[ Since a² - b² = ( a + b ) ( a - b ) ]

( √3 ) ( CosecX - CotX ) = 1 from ( 1 )

CosecX - CotX = 1 / √3 -----( 2 )

Add equations ( 1 ) and ( 2 ) we get,

2CosecX = √3 + 1 /√3

= ( 3 + 1 ) / √3

= 4 / √3

Therefore,

CosecX = 4 /2√3

CosecX = 2 / √3

CosecX = Cosec 60°

X = 60°

Answer 2

Hope this Helps :)

For the (ii) part,

Cosec^2 (X) - cot^2 (X) = 1

=> (Cosecx - Cotx )(Cosecx + Cotx)=1