If cos[2sin-1(x)]=19, then x=?
only 23
only -23
23,-23
Neither 23 nor -23
Explanation for the correct option:
Step 1. Find the value of x:
Given, cos[2sin-1(x)]=19
Let sin-1(x)=A
⇒ sinA=x ….(i)
Step 2. By Substituting sin-1(x)=A in the given equation, we get
cos2A=19
⇒1–2sin2A=19
⇒ 2sin2A=1–19
⇒ 2sin2A=89
⇒ sin2A=49
⇒ sinA=49
=±23 ….(ii)
Step 3. By equating equation (i) and (ii), we get
x=23,-23
Hence, Option ‘C’ is Correct.
If f=x1+x2+13(x1+x2)3+15(x1+x2)5+... to ∞ and g=x−23x3+15x5+17x7−29x9+..., then f=d×g. Find 4d.