NDA Mathematics Question (2025) — Solution

Step-by-step solution

Given p = cosec \, 20^ = 1 20^ and q = cosec \, 70^ = 1 70^ = 1 20^ Substituting p and q into the given expression: 3 \,p 4 - q 4 = 3 4 20^ - 1 4 20^ Taking the common denominator: = 3 20^ - 20^ 4 20^ 20^ Multiplying and dividing the numerator by 2, and rewriting the denominator: = 2 ( 3 2 20^ - 1 2 20^ ) 2 (2 20^ 20^ ) Using the identities 60^ = 3 2 , 60^ = 1 2 , and 2 = 2 : = 2 ( 60^ 20^ - 60^ 20^ ) 2 40^ Using the identity (A - B) = A B - A B: = 2 (60^ - 20^ ) 2 40^ = 2 40^ 2 40^ = 1 Answer: 1