Question

if cosec theta - sin theta = m and sec theta - cos theta = n
then show that (m^2n)^2/3 + (mn^2)^2/3 = 1.
please solve this question.
need it urgently​. correct answer will be marked as brainiest and will be followed. anyone can solve.

Aradhana can you please solve.

please solve this question fast

Answer 1

Given that:

m = cosec Ø - sin Ø

n = sec Ø - cos Ø

To prove:

(m^2n)^2/3 + (mn^2)^2/3

Proof:

m = 1/sin Ø - sin Ø = cos^2 Ø/sin Ø

n = 1/cos Ø - cos Ø = sin^2 Ø/cos Ø

(m^2n)^2/3 + (mn^2)^2/3

=> [(cos^4 Ø/sin^2 Ø)(sin^2 Ø/cos Ø)]^2/3 + [(sin^4 Ø/cos^2 Ø)(cos^2 Ø/sin Ø)]^2/3

=> (cos^3 Ø)^2/3 + (sin^3 Ø)^2/3

=> cos^2 Ø + sin^2 Ø

=> 1

Hence Proved! ✓