Question

Which of the following identities does not hold?

• A. sin^–1 x = cot^–1$\left\lbrack \frac{\sqrt{(1 - x^{2})}}{x} \right\rbrack$; 0 < x £ 1
• B. sin^–1 x = cot^–1$\left\lbrack \frac{\sqrt{(1 - x^{2})}}{x} \right\rbrack$; –1 £ x < 0
• C. sin^–1 x = cos^–1$\sqrt{(1 - x^{2})}$; 0 £ x £ 1
• D. sin^–1 x =1– sin^–1(–x); – 1 £ x £ 1

Answer 1

Answer: (B)

sin^–1 x = cot^–1$\left\lbrack \frac{\sqrt{(1 - x^{2})}}{x} \right\rbrack$; –1 £ x < 0

Answer 2

L.H.S. of choice (2) is a negative number and R.H.S. is a positive number.