Question

tan theata + cot theta=6, then prove that tan²theata + cot²theta=34​

Answer 1

$\huge{\mathcal{\blue{Answer}}}$

$(tan + cot) {}^{2} = tan {}^{2} + cot {}^{2} + 2(tan)(cot) \\ (6) {}^{2} = tan {}^{2} + cot {}^{2} + 2( \frac{sin}{cos} \times \frac{cos}{sin} ) \\ 36 = tan {}^{2} + cot {}^{2} + 2 \\ 36 - 2 = tan {}^{2} + cot {}^{2} \\ 34 = tan {}^{2} + cot {}^{2}$