Question

tan theta upon 1 + cot theta + cot theta upon 1 + 10 theta

Answer 1

hope it is helpful !

Answer 2

HOLA

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$\frac{tan \: }{1 \: + \: cot} \: + \: \frac{cot}{1 \: + \: tan \:} \\ \\ tan \: = \: \frac{sin}{cos \:} .. \: cot \: = \: \frac{cos}{sin} \\ \\ tan \: + \: cot \: = \: sin {}^{2} \: + \: cos {}^{2} = 1 \\ \\ 1 \: + \: cot \: = \: 1 \: + \: \frac{cos}{sin} \\ \\ 1 \: + \: tan \: = \: 1 \: + \: \frac{sin}{cos} \\ \\ 1 \: + \: tan \: + \: 1 \: + \: cot \: = \: 1 \: + \: \frac{sin}{cos} \: + \: 1 \: + \frac{cos}{sin} \\ \\ = \: sin {}^{2} + \: cos {}^{2} = \: 1 \: \\ \\ hence \: \frac{tan}{ \: 1 \: + \: cot} + \: \frac{cot}{1 \: + \: tan} = \: 1$
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