Question

Prove that
Cos70°/Sin20°+Cos59°/Sin31°-8Sin²30°

Answer 1

HELLO DEAR,

I think something is mistake in your questions

right questions is like this

Cos70°/Sin20°+Cos59°/Sin31°=8Sin²30°
$\frac{ \cos(70) }{ \sin(20) } + \frac{ \cos(59) }{ \sin(31) } \\ = > \frac{ \cos(90 - 20) }{ \sin(20) } + \frac{ \cos(90 - 31) }{ \sin(31) } \\ = > \frac{ \sin(20) }{ \sin(20) } + \frac{ \sin(31) }{ \sin(31) } \\ = > 1 + 1 = 2..........(1)$





$8 \times \sin ^{2} 30 = 8 \times {( \frac{1}{2} })^{2} \\ = > 8\times \frac{1}{4} \\ = > 2........(2)$
from--(1)and--(2)

we get,

Cos70°/Sin20°+Cos59°/Sin31°=8Sin²30°

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

ANSWER
........





=>​sin(20)​​cos(90−20)​​+​.
sin(31)​​cos(90−31)


​​​=>​sin(20)​​sin(20)​​+​sin(31)​​sin(31)​​​=>1+1=2



​8×sin​2​​30=8×2​​​. = >8×​4​​1​​​=>2......

we get,

Cos70°. Cos59
_____. +. ________
Sin20° Sin31°=8Sin²30°

.