If tan theta + cot theta = 4,then tan^{4} the | vedclass

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(A) Given: $	an 	heta + \cot 	heta = 4$ Squaring both sides,we get: $(	an 	heta + \cot 	heta)^{2} = 4^{2}$ $	an^{2} 	heta + \cot^{2} 	heta +

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$194$

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(A) Given: $	an 	heta + \cot 	heta = 4$ Squaring both sides,we get: $(	an 	heta + \cot 	heta)^{2} = 4^{2}$ $	an^{2} 	heta + \cot^{2} 	heta + 2 	an 	heta \cot 	heta = 16$ Since $	an 	heta \cot 	heta = 1$,we have: $	an^{2} 	heta + \cot^{2} 	heta + 2(1) = 16$ $	an^{2} 	heta + \cot^{2} 	heta = 14$ Squaring both sides again: $(	an^{2} 	heta + \cot^{2} 	heta)^{2} = 14^{2}$ $	an^{4} 	heta + \cot^{4} 	heta + 2 	an^{2} 	heta \cot^{2} 	heta = 196$ $	an^{4} 	heta + \cot^{4} 	heta + 2(1)^{2} = 196$ $	an^{4} 	heta + \cot^{4} 	heta = 196 - 2 = 194$

If $\tan \theta + \cot \theta = 4$,then $\tan^{4} \theta + \cot^{4} \theta = $

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