Question

please answer fast 2+tan²a+cot²a=1/sin²a-sin⁴a prove​

Answer 1

Step-by-step explanation:

to show 2+tan²a+cot²a=1/sin²a-sin⁴a

2+tan²a+cot²a=1+tan²a+1+cot²a=sec²a+cosec²a

=1/cos²a+1/sin²a

=sin²a+cos²a/(cos²asin²a)

=1/(1-sin²a)(sin²a) since 1-sin²a=cos²a

=1/(sin²a-sin⁴a)

Answer 2

$2 + {tan}^{2} a + {cot}^{2} a \\ \\ = 1 + {tan}^{2} a + 1 + {cot}^{2} a \\ \\ = {sec}^{2} a + {cosec}^{2} a \\ \\ = \frac{1}{ {sin}^{2} a {cos}^{2} a} \\ \\ = \frac{1}{ {sin}^{2} a(1 - {sin}^{2}a) } \\ \\ = \frac{1}{ {sin}^{2} a - {sin}^{4}a }$