Question

the value of 9/cot2theta- 9/ cosec2theta is​

Answer 1

Step-by-step explanation:

$\frac{9}{ {cot}^{2} \theta } - \frac{9}{ {cosec}^{2} \theta } \\ \\ = \frac{9 \: {cosec}^{2} \theta - 9 \: {cot}^{2} \theta}{ {cot}^{2} \theta \times {cosec}^{2} \theta } \\ \\ = \frac{9 \: ( {cosec}^{2} \theta - {cot}^{2} \theta)}{ {cot}^{2} \theta\times {cosec}^{2} \theta } \\ \\ = \frac{9 \: \times 1}{ {cot}^{2} \theta\times {cosec}^{2} \theta } \\ \\ = 9 \times {tan}^{2} \theta \times {sin}^{2} \theta \\ \\ = 9 \: {tan}^{2} \theta \: {sin}^{2} \theta \\ \\ \purple {\boxed {\boxed {\boxed {\therefore \: \frac{9}{ {cot}^{2} \theta } - \frac{9}{ {cosec}^{2} \theta } = 9 \: {tan}^{2} \theta \: {sin}^{2} \theta}}}}$