If we put A= 45 degree then also same answer coming, but if we put A= 30 or 60 degrees then why diff answer is coming

Question

What are those factors to be borne in mind while value putting, for example what should we consider to choose A= 45 degrees rather 30 or 60 degrees

Answer 1

The identity is true for all values of A, so let’s see where the reasoning is faulty.

If A=30, sinA=½, cscA=2, cosA=√3/2, secA=2/√3, tanA=1/√3, cotA=√3.

(secA-cosA)²=4/3-2+3/4=1/12, (cscA-sinA)²=4-2+1/4=9/4, (cotA-tanA)²=3-2+1/3=4/3.

So 1/12+9/4-4/3=(1+27-16)/12=12/12=1.

If A=60, sinA=√3/2, cscA=2/√3, cosA=½, secA=2, tanA=√3, cotA=1/√3.

(secA-cosA)²=4-2+1/4=9/4, (cscA-sinA)²=4/3-2+3/4=1/12, (cotA-tanA)²=1/3-2+3=4/3.

9/4+1/12-4/3=1 as before.

So the identity is true for A=30, 60 and any other value (perhaps we should avoid 0 and 90).