Question

sin^2 theta = cos^3 theta prove cot^6 theta-cot^2 theta=1

Answer 1

given,
sin²∅ = cos³∅
divide both sides, by sin²∅

sin²∅/sin²∅ = cos³∅/sin²∅
1 = cos²∅.cos∅/sin²∅
1 = cot²∅.cos∅
1/cos∅ = cot²∅
sec∅ = cot²∅
take square both sides,

sec²∅ = cot⁴∅
we know, sec²∅ = 1 + tan²∅ use, this
1 + tan²∅ = cot⁴∅
1 + 1/cot²∅ = cot⁴∅
cot²∅ + 1 = cot^6∅
cot^6∅ - cot²∅ = 1

hence proved //