If tan theta + cot theta = 2,then the value o | vedclass

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(A) Given that $	an 	heta + \cot 	heta = 2$.Since $\cot 	heta = \frac{1}{	an 	heta}$,we can write the equation as $	an 	heta + \frac{1}{	an \

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$2$

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(A) Given that $	an 	heta + \cot 	heta = 2$.Since $\cot 	heta = \frac{1}{	an 	heta}$,we can write the equation as $	an 	heta + \frac{1}{	an 	heta} = 2$.Multiplying both sides by $	an 	heta$,we get $	an^2 	heta + 1 = 2 	an 	heta$.Rearranging the terms,we get $	an^2 	heta - 2 	an 	heta + 1 = 0$.This is a perfect square: $(	an 	heta - 1)^2 = 0$.Therefore,$	an 	heta = 1$.Since $	an 	heta = 1$,then $\cot 	heta = \frac{1}{1} = 1$.Now,substituting these values into the expression $	an^{100} 	heta + \cot^{100} 	heta$,we get $1^{100} + 1^{100} = 1 + 1 = 2$.

If $\tan \theta + \cot \theta = 2$,then the value of $\tan^{100} \theta + \cot^{100} \theta$ is

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