Consider the following statements: 1. There exists θ ∈(-(π)/(2),...
Consider the following statements:
1. There exists θ∈(−2π,2π) for which tan−1(tanθ)=θ.
2. sin−1(31)−sin−1(51)=sin−1(1522(3−1))
Which of the above statements is/are correct?
Options
A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2
Correct answer
B. 2 only
Step-by-step solution
θ∈(−2π,2π) for which tan−1(tanθ)=θ
Hence, statement (1) is incorrect.
if x≤1;y≤1∴sin−1(x)−sin−1y=sin−1[x1−y2−y1−x2]x2+y2≤1⇒sin−131−sin−151=sin−1[311−251−511−91]=sin−1[3×5124−5×318]=sin−1[158×3−8]=sin−1[1522(3−1)]$
Hence, statement (2) is correct.
