Question

prove that tan15+cot15=4

Answer 1

tan 15 + cot 15
= sin 15 / cos 15 + cos 15 / sin 15
= (sin²15 + cos²15) / (sin 15 cos 15)
= 1 / (1/2 sin 30)
= 2 / sin 30
= 2 / (1/2)
= 4

Answer 2

lhs = tan 15 +cot 15

= tan 15 +1/tan 15[here we used cot x = 1/tan x]
= (tan² 15 +1)/tan 15
= sec²15/tan 15[ here we used 1+ tan² x= sec² x]

= 1/cos²15 *cos 15/sin 15[cancellation of cos 15 we get]
=1/cos 15*sin 15

= 2/(2 sin 15 *cos 15) [multiply numerator and denominator with 2]

= 2/sin (2*15)[ here we used 2 sinx cos x= sin 2x]
= 2/sin 30

= 2/(1/2) [ here sin 30 = 1/2]
= 2*2
=4
=rhs