Question

If cot alpha + beta is equal to zero then find the value of sin alpha + 2 beta

Answer 1

Answer:

$cot \: ( \alpha + \beta ) = 0 \\ \implies \: cot \: ( \alpha + \beta ) =cot \: {90}^{0} \\ \implies \: \alpha + \beta = {90}^{0} \\ \implies \: \beta = {90}^{0} - \alpha \\ \implies \: 2\beta = {180}^{0} - 2\alpha \\ \alpha + 2 \beta = \alpha + {180}^{0} - 2\alpha \\ = {180}^{0} - \alpha \\ sin \: (\alpha + 2 \beta) \: = sin \: ({180}^{0} - \alpha) \\ = sin \: \alpha$