Question

11. Evaluate :
sin2 34° + sin2 56° + 2 tan 18° tan 72° - cot 30°​

Answer 1

$= {sin}^{2} 34 + {sin}^{2} 56 + 2 \: tan \: 18 \: tan \: 72 - cot30 \\ = {cos}^{2} (90 - 34) + {sin}^{2} 56 + 2 \: cot(90 - 18)tan72 - cot30 \\ = {cos}^{2} 56 + {sin}^{2} 56 + 2 \: cot \: 72 \: tan \: 72 - cot \: 30 \\ = 1 + 2 - \sqrt{3} \\ = 3 - \sqrt{3} \\ \\ {sin}^{2} a + {cos}^{2} a = 1 \\ tan \: a \: cot \: a = 1 \\ cot \: 30 = \sqrt{3} \\ \\ i \: have \: used \: these \: three \: identities. \\ if \: you \: do \: not \: understand \: please \: \\ look \: at \: these \: three \: identities$