Question

Cosec A + CotA = m
Show that (m^2 - 1) + ( m^2 + 1 ) = cos A

Answer 1

Answer:

Step-by-step explanation:cosec A + cot A =m-----(1)

lhs = (m²-1)/(m²+1)

= [(cosec A+cot A)² - 1]/[(cosec A +cot)²+1] from (1)

= [ cosec² A +2cosecAcotA+cot² A-1]/[cosec²A +2cosec AcotA+cot ²A +1]

= [(cosec ²A-1 )+2cosec AcotA+cot²A]/[cosec²A +2cosecAcotA +(cot²A+1)]

= [cot²A+2cosecAcotA+cot²A]/[cosec²A+2cosecAcotA+cosec²A]

{since cosec²A-1 = cot²A and cot²A +1 = cosec²A]

=[2cot²A+2cosecAcotA]/[2cosec²A+2cosecAcotA]

=[2cotA(cotA+cosecA)]/ [2cosecA(cosecA+cotA)]

after cancellation

=cotA/cosecA

=(cosA/sinA)/(1/sinA)

= cosA

=rhs