Question

if tan0+cot0=4 than find the value of tan4 0+cot 4 0

please slove this ​

Answer 1

$\huge{\underline{\underline{\bf Identities\:used}}}$

$\underline\pink{\boxed{\bf (a+b)² = a²+b²+2ab}}$

$\implies \tan( \theta) + \cot( \theta) = 4 \\ \\ \implies( \tan^{2} ( \theta) + \cot^{2} ( \theta) + 2 \tan( \theta) \cot( \theta) ) = 16 \\ \\ \implies\tan^{2} ( \theta) + \cot^{2} ( \theta) = 14 \: - - - (1) \\ \\ \implies\tan^{4} ( \theta) + \cot^{4} ( \theta) \\ \\ \implies (\tan^{2} ( \theta))^{2} + (\cot^{2} ( \theta))^{2} \\ \\\implies (\tan^{2} ( \theta) + \cot^{2} ( \theta)) - 2\tan^{2} ( \theta) \cot^{2} ( \theta) \\ \\ \implies(14) ^{2} - 2 = 194$