cot 105 - tan 105= 2√3
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cot105° - tan105° = cot(60+45)° - tan(60+45)°
=>[(cot60°.cot45°-1)/(cot60°+cot45°)] - [(tan60°+tan45°)/(1-tan60°.tan45°)]
=> [(1- √3)/(1+√3)] - [(1+ √3)/(1- √3)]
=> [(1- √3)/(1+√3)] + [(1+ √3)/(√3 - 1)]
=>[(√3 -1–3+√3 + 1+3+2√3)/(3–1)]
=>[4√3/2]
=>2√3
Hence Proved.
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=>[(cot60°.cot45°-1)/(cot60°+cot45°)] - [(tan60°+tan45°)/(1-tan60°.tan45°)]
=> [(1- √3)/(1+√3)] - [(1+ √3)/(1- √3)]
=> [(1- √3)/(1+√3)] + [(1+ √3)/(√3 - 1)]
=>[(√3 -1–3+√3 + 1+3+2√3)/(3–1)]
=>[4√3/2]
=>2√3
Hence Proved.
I hope it helps u...
please mark me as brainliest...
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