Question

cosec 10° - ✓3 sec 10 = 4​

Answer 1

Answer:

$lhs = \cosec10 - \sqrt{3} \sec10 \\ \\ = \frac{1}{ \sin10} - \frac{ \sqrt{3} }{ \cos10 } \\ \\ = \frac{ \cos10 - \sqrt{3} \sin10 }{ \sin10\cos10 } \\ \\ = 2 \: \: (\frac{ \cos10 - \sqrt{3} \sin10 }{2 \sin10 \cos10 }) \\ \\ = 2 \times 2( \frac{ \frac{1}{2} \cos10 - \frac{ \sqrt{3} }{2} \sin10 }{ \sin(2×10)} ) \\ \\ = 4 \times \frac{ \sin30 \cos10 - \sin10 \cos30 }{ \sin20 } \\ \\ = 4 \times \frac{ \sin(30 - 10) }{ \sin20 } \\ \\ = 4 \times \frac{ \sin20 }{ \sin20 } \\ \\ = 4 \\ \\ = rhs$