Question

prove that sin^2 ∅ (1-cot^2 ∅ )=1

Answer 1

$LHS = Sin^2\phi(1-Cot^2\phi)$

$= Sin^2\phi(1-\frac{Cos^2\phi}{Sin^2\phi})$

$= Sin^2\phi - Cos^2\phi$

So the question must be having a mistake because

$Sin^2\phi - Cos^2\phi \neq 1$

If the question is to prove

$Sin^2\phi(1+Cot^2\phi) = 1$,

then following the same steps above will arrive at

$Sin^2\phi + Cos^2\phi$, which is equal to one

HOPE THIS HELPS