Consider the following : 1. A/1- A+ A/1- A = A+ A 2. (1- A- A)² =2(1- A)(1+ A) Which of the above is /are identity/identities?

CDS 2015 PYQ with Answer — Consider the following : 1. A/1- A+ A/1- A = A+ A 2. (1- A- A)² =2(1-…

2015 · Q68

Consider the following :

1A/1- A+ A/1- A = A+ A
2(1- A- A)² =2(1- A)(1+ A)

Which of the above is /are identity/identities?

Elementary MathematicsTrigonometry

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Explanation

Statement 1 is the standard identity tanA/(1−cotA) + cotA/(1−tanA) = 1 + tanA + cotA (the 'cot' labels are dropped in the source) — true. Statement 2, (1−sinA−cosA)² = 2(1−sinA)(1+cosA), fails (e.g. at A = 0: LHS 0 ≠ RHS 4) — false. Hence '1 only' (option A).