Question

tan20° + 4 sin20°= 3^1/2​

Answer 1

Hey Pretty Stranger!

Here we have to prove that tan20° + 4sin20° = √3

Uhh.. uhh.. why do we need to prove everything, well, let's do it ._.

→ tan20 + 4sin20

→ sin20/cos20 + 4sin20

→ (sin20 + 4sin20cos20)/cos20

→ sin 20 + 2 sin 40)/ cos 20

→ (sin 20 + 2 sin (60-20))/ cos 20

→ ( sin 20 + 2 sin 60 cos 20 - 2 cos 60 sin 20)/ cos 20

→ (sin 20+ 2 sin 60 cos 20 - sin 20)/ cos 20

→ 2 sin 60cos 20/ cos 20

→ 2 sin 60

→ 2(√3/2)

→ √3

$\sf\: Hence,\: proved.$

Yayyy, We did it!

Answer 2

Answer:

tan20° + 4 sin20°

= sin20/cos20 + 4 sin20°

= (sin20° +4sin20° +cos20° ) / cos20°

= (sin20° +2sin40°) / cos20°

= (sin20° + 2sin(60-20)) / cos20°

= sin20°+ 2sin60° cos20°  - 2sin20° cos60°  / cos20°

= sin20° + 2(√3/2) cos 20° - 2sin20° (1/2) / cos20°

= sin 20+ √3 cos20°  - sin20°  / cos20°

= √3 cos20°  / cos20°

= √3 = (3)^1/2

Step-by-step explanation:

Hope it helps you :)