Question

if sin theta + cos theta is equal to root 3 find tan theta + cot theta

Answer 1

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Answer 2

sin A + cos A= √3
${(sin \: a + cos \: a)}^{2} = \sqrt{ {3}^{2} } \\ {sin}^{2} a \: + {cos}^{2} a + 2sin \: a \times cos \: a= 3 \\ 2sin \: a \: cos \: a = 3 - 1 \\ sin \: a \times cos \: a = \frac{2}{2} = 1 \\ \\ tan \: theta + cot. \:theta ==> \frac{sin \: a}{cos \: a} + \frac{cos \: a}{sin \: a} \\ \frac{ {sin \: }^{2} a+ {cos \: }^{2}a }{sin \: a \times cos \: a} = \frac{1}{1} = 1$
value of tan theta+ cot theta is 1