Q

Asked by araima2001 | 9th Sep, 2016, 11:11: AM

Expert Answer:

 
tan straight theta over 2 space equals space cosecθ minus sinθ

rightwards double arrow tan straight theta over 2 equals fraction numerator 1 plus tan squared straight theta over 2 over denominator 2 tan straight theta over 2 end fraction minus fraction numerator 2 tan straight theta over 2 over denominator 1 plus tan squared straight theta over 2 end fraction
rightwards double arrow open parentheses 2 tan squared straight theta over 2 close parentheses open parentheses 1 plus tan squared straight theta over 2 close parentheses equals open parentheses 1 minus tan squared straight theta over 2 close parentheses squared

Let space tan squared straight theta over 2 space equals space straight x
rightwards double arrow 2 straight x open parentheses 1 plus straight x close parentheses equals open parentheses 1 minus straight x close parentheses squared
rightwards double arrow straight x squared plus 4 straight x minus 1 equals 0
rightwards double arrow straight x equals negative 2 plus-or-minus square root of 5
rightwards double arrow straight x equals negative 2 plus square root of 5 space space space............ open parentheses as space straight x space greater or equal than space 0 close parentheses
rightwards double arrow space tan squared straight theta over 2 equals negative 2 plus square root of 5

sec squared straight theta over 2 equals 1 plus tan squared straight theta over 2 equals 1 plus negative 2 plus square root of 5 equals square root of 5 minus 1

Option space straight B space is space correct.

Answered by Vijaykumar Wani | 14th Sep, 2016, 12:19: PM