show that 1/sin10-root3/cos10=4
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1/ sin10° - √3 /cos10°
=> (cos10° -√3.sin10°)/sin10°.cos10°
use
sin2A =2sinA.cosA
and sin(A-B) =sinA.cosB -cosa.sinB
now,
=> 4(1/2cos10° -√3/2sin10°)/2sin10°.cos10°
=> 4{sin30°.cos10° -cos30.sin10°}/sin20°
=>4sin(30°-10°)/sin20°
=>4sin20°/sin20°
=>4 = RHS
=> (cos10° -√3.sin10°)/sin10°.cos10°
use
sin2A =2sinA.cosA
and sin(A-B) =sinA.cosB -cosa.sinB
now,
=> 4(1/2cos10° -√3/2sin10°)/2sin10°.cos10°
=> 4{sin30°.cos10° -cos30.sin10°}/sin20°
=>4sin(30°-10°)/sin20°
=>4sin20°/sin20°
=>4 = RHS
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