`cos ((3pi)/(2)+theta) cos (2pi+theta)``xx [ cot ((3pi)/(2) -theta) + cot (2pi + theta) ] = ?`

Options

A. `0`
B. `1`
C. `sin theta`
D. `cos theta`

Answer

B

Explanation

We have
`"cos " ((3pi)/(2) + theta) "cos " (2pi +theta) [ "cot " ((3pi)/(2)-theta) + " cot " (2pi + theta) ]`
`= " cos " (pi + ((pi)/(2) + theta) ] " cos " (2pi + theta) [ " cot " { pi + ((pi)/(2)-theta) } " cot " (2pi + theta) ]`
` =- " cos " ((2pi)/(2) " cos " theta) [ " cot " ((pi)/(2) = theta) + " cot " theta]`
`[ :' " cos " (pi + x) = " cos x , cot " (pi + x) = " cot x and cot " (2pi + x) " cot x " ]`
`= " sin " theta " cos " theta [ " tan " theta + " cot " theta] [ :' " cos " ((pi)/(2) + theta) =- " sin " theta]`
`=( " sin " theta " cot " theta) [("sin "theta)/("cos " theta) + (" cos " theta)/("sin " theta)] = ( "sin " theta " cos " theta) . (("sin"^(2) theta " cos"^(2) theta))/(("sin " theta " cos " theta)) =1`