Question

Find tan 15 degree and hence show that tan 15 +cot 15=4

Answer 1

Step-by-step explanation:

tan15 = tan(45-30)

= tan45 - tan30/1+tan45*tan30

=( 1 - 1/3½)/(1 + 1/3½)

=( 3½ - 1/3½) /(3½+1/3½)

= 3½ - 1 / 3½ + 1

= (3½ - 1 / 3½+1) *(3½-1/3½-1)

= (3½-1)²/3-1

= (3 + 1 - 2*3½)/2

=(4 - 2*3½)/2

= 2 - 3½

cot15 = cot(45-30)

= cot45*cot30+1/cot45-cot30

= (3)½+1/(3)½-1 * (3)½+1/(3)½+1

= (3½+1)² / 3-1

= 3 + 1 + 2*3½/2

= 4 + 2*3½/2

= 2 + 3½

tan15 + cot15 = 2 - 3½ + 2 + 3½

= 4

hence proof