Question

Prove that:-. no spam otherwise Account will be deleted..no spam .​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\\ \small \sf{l.h.s = \frac{ {cos}^{2}(45 + \theta) + {cos}^{2}(45 - \theta) }{tan(60 + \theta)tan(30 - \theta)} } \\ \\ \\ \bigstar\boxed{ \bf{sin \theta = cos(90 - \theta)}} \\ \\ \bigstar \boxed{ \bf{cot \theta = tan(90 - \theta)}} \\ \\ \\ = \small \sf \frac{ {cos}^{2}( 45 + \theta) + {sin}^{2}(90 - (45 + \theta)) }{tan(60 + \theta)cot(90 - (30 - \theta))} \\ \\ \\ = \sf\frac{ {cos}^{2} (45 + \theta) + {sin}^{2}(45 - \theta) }{tan(60 + \theta)cot(60 + \theta)} \\ \\ \\ \bigstar\boxed{ \bf{ {cos}^{2} \theta + {sin}^{2} \theta = 1 }} \\ \\ \bigstar\boxed{ \bf{tan \theta = \frac{1}{cot \theta} }} \\ \\ \\ \sf = \frac{1}{ \cancel{tan(60 + \theta) }(\frac{1}{ \cancel{tan(60 + \theta)}) } } \\ \\ \\ = \sf 1 \: = r.h.s \: \: \: \: \: \: (proved)$