( y ) \operatorname { cot } \theta \operatorname { cot } 3 \theta - \o

1.	( y ) \operatorname { cot } \theta \operatorname { cot } 3 \theta - \operatorname { cot } 3 \theta \operatorname { cot } 4 \theta - \operatorname { cot } \theta \operatorname { cot } 4 \theta = 1
Answer» LHS = cot A . cot 2A − cot 2A . cot 3A − cot 3A . cot A =cot A . cot 2A − cot 3A(cot 2A + cot A) =cot A . cot 2A − cot (2A + A)(cot 2A + cot A) =cot A . cot 2A − [cot 2A . cot A − 1cot 2A + cot A](cot 2A + cot A) =cot A . cot 2A − cot 2A . cot A + 1 =1 =RHS

( y ) \operatorname { cot } \theta \operatorname { cot } 3 \theta - \operatorname { cot } 3 \theta \operatorname { cot } 4 \theta - \operatorname { cot } \theta \operatorname { cot } 4 \theta = 1

Answer»

LHS = cot A . cot 2A − cot 2A . cot 3A − cot 3A . cot A

=cot A . cot 2A − cot 3A(cot 2A + cot A)

=cot A . cot 2A − cot (2A + A)(cot 2A + cot A)

=cot A . cot 2A − [cot 2A . cot A − 1cot 2A + cot A](cot 2A + cot A)

=cot A . cot 2A − cot 2A . cot A + 1

=1 =RHS