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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

## Answers

Answered by

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****!**** ****✓**

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