Question

Cot54 cot36 + tan20 tan70

Answer 1

cot54.cot36+tan20.tan70

=1/tan54.tan (90-36)+tan20.1/cot70

=1/tan54.tan54+tan20.1/tan20

=1+1

=2

for these sum you have to know

cot A= tan (90-A)

Answer 2

Hi !

cotA = tan ( 90 - A)

cot 36 = tan (90 - 36) = tan 54

similarly,

tan A = cot (90 - A)

tan 70 = cot ( 90 - 70) = cot 20

We know that ,

tan A * cot A = 1

cot 54*cot36 + tan20*tan70

cot54* tan 54 + tan20*cot20

1 + 1

= 2

Hence,


Cot54 cot36 + tan20 tan70 = 2