Question

PLEASE HELPPPPPPP MEEEEEE

Answer 1

tan (π/6) + sin (5π/3) . cos (- 3π/4)

= tan 30° + sin 300° . cos (- 135°)

= tan 30° + sin (360° - 60°) . cos 135°

= tan 30° + (- sin 60°) . cos (180° - 45°)

= tan 30° + (- sin 60°) . (- cos 45°)

= tan 30° + sin 60° . cos 45°

= (1/3)√3 + (1/2)√3 . (1/2)√2

= (1/3)√3 + (1/4)√6

= (4/12)√3 + (3/12)√6

= (4√3 + 3√6)/12

Answer 2

Answer:

Option 2

Step-by-step explanation:

tan(pi/6) = 1/sqrt(3) = sqrt(3)/3

sin(5pi/3) = -sin(pi/3) = -sqrt(3)/2

cos(-3pi/4) = cos(pi/4) = -1/sqrt(2)

= -sqrt(2)/2

sqrt(3)/3 + -sqrt(3)/2 × -sqrt(2)/2

sqrt(3)/3 + sqrt(6)/4

Lcm: 12

[4sqrt(3) + 3sqrt(6)]/12