Question

If sin α sin β – cos α cos β + 1 =0, then prove that cot α tan β = -1.

Answer 1

Answer:

Step-by-step explanation:

(sin α sin β – cos α cos β) + 1 =0

• taking the brackets to the RHS

1 = -(sin α sin β – cos α cos β)

• distributing the - sign

1 = - sin α sin β + cos α cos β

cos 0 = cos (α + β)

α + β = 0

α = - β

• Now solving cot α tan β

cot α = 1 / tan α

• and α = - β

cot α = 1/ tan (-β)

cot α = -1/ tan β

(-1/ tan β ) × tan β

• cancelling the tan  β

= - 1

LHS = RHS

Hence, proved