Question

tan²∅ - sec²∅/ cot²∅ - cosec²∅ =?​

Answer 1

Answer:

Let theeta = a

tan²∅ - sec²∅/ cot²∅ - cosec²∅

$\frac{ \frac{ { \sin}^{2} (a)}{ { \cos }^{2}(a) } - \frac{1}{ { \cos}^{2} (a)} }{ \frac{ { \cos}^{2} (a)}{ { \sin }^{2} (a)} - \frac{1}{ { \sin}^{2} (a)} } \\ = \frac{ \frac{ { \sin(a) }^{2} - 1}{ { \cos(a) }^{2} } }{ \frac{ { \cos(a) }^{2} - 1}{ { \sin(a) }^{2} } } \\ = \frac{ \frac{ - {( \cos(a) }^{2} )}{ { \cos(a) }^{2} } }{ \frac{ - ( { \sin(a) }^{2} )}{ { \sin(a) }^{2} } } \\ = \frac{ - 1}{ - 1} = 1$

Hence, tan²∅ - sec²∅/ cot²∅ - cosec²∅ = 1