prove that cosec10 - root3sec10.=4
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cosec10-root3 sec10=4
LHS=1/sin10 - root3/cos10
=(cos10-root3 sin10)/sin10.cos10
=2(1/2.cos10-root3/2.sin10)/{1/2(2sin10.cos10)}
=2 (sin30.cos10-cos30.sin10)/(1/2sin20)
=4sin (30-10)/sin20
=4sin20/sin20=4=RHS
LHS=1/sin10 - root3/cos10
=(cos10-root3 sin10)/sin10.cos10
=2(1/2.cos10-root3/2.sin10)/{1/2(2sin10.cos10)}
=2 (sin30.cos10-cos30.sin10)/(1/2sin20)
=4sin (30-10)/sin20
=4sin20/sin20=4=RHS
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