Question

Prove that $\frac{1}{sin 10\textdegree} - \frac{\sqrt{3}}{cos 10\textdegree}$ = 4

Answer 1

LHS = 1/sin10° - √3/cos10°

= (cos10° - √3sin10°)/sin10° cos10°

= 2(1/2 cos10° - √3/2 sin10°)/sin10° cos10°

[ we know, cos30° = √3/2

and sin30° = 1/2 ]

= 2 × 2(sin30° cos10° - cos30° sin10°)/(2sin10° cos10°)

from formula,sin30° cos10° - cos30° sin10° = sin(30° -10°) = sin20°

and 2sin10° cos10° = sin20°

= 4sin20°/sin20°

= 4 = RHS [ hence proved]

Answer 2

HELLO DEAR,



1/sin10° - √3/cos10°

=> (cos10° - √3sin10°)/sin10° cos10°

=> 2(1/2 cos10° - √3/2 sin10°)/sin10° cos10°

[ we know, cos30° = √3/2 and sin30° = 1/2 ]

=> 2 * 2(sin30° cos10° - cos30° sin10°)/(2sin10° cos10°)

[ as,sin30° cos10° - cos30° sin10° = sin(30° -10°) = sin20° and 2sin10° cos10° = sin20° ]

= 4sin20°/sin20°

= 4


I HOPE IT'S HELP YOU DEAR,
THANKS