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Given that,
tan (A + B) = (tanA + tanB)/(1 - tanA tanB)
We need to find tan75°
= tan (45° + 30°)
= (tan45° + tan30°)/(1 - tan45° tan30°)
= (1 + 1/√3)/(1 - 1/√3)
= (√3 + 1)/(√3 - 1)
= (√3 + 1)/(√3 - 1) * (√3 + 1)/(√3 + 1)
= (3 + 2√3 + 1)/(3 - 1)
= (4 + 2√3)/2
= 2 + √3
tan (A + B) = (tanA + tanB)/(1 - tanA tanB)
We need to find tan75°
= tan (45° + 30°)
= (tan45° + tan30°)/(1 - tan45° tan30°)
= (1 + 1/√3)/(1 - 1/√3)
= (√3 + 1)/(√3 - 1)
= (√3 + 1)/(√3 - 1) * (√3 + 1)/(√3 + 1)
= (3 + 2√3 + 1)/(3 - 1)
= (4 + 2√3)/2
= 2 + √3
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Shobhit1903:
Answer is 2+√3
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