Which of the following is/are true? (i) sin -1 x+ cos -1 x=(π/2), x ∈[-1,1] (ii) tan -1 x+ cot -1 x=(π/2), x ∈ R (iii) operatornamecosec-1 x+ sec -1 x=(π/2),|x| ≥ 1

Question

Which of the following is/are true? (i) sin -1 x+ cos -1 x=(π/2), x ∈[-1,1] (ii) tan -1 x+ cot -1 x=(π/2), x ∈ R (iii) operatornamecosec-1 x+ sec -1 x=(π/2),|x| ≥ 1 (A) (i), (ii) (B) (ii), (iii) (C) (i), (iii) (D) (i), (ii), (iii)

Tardigrade Admin · Accepted Answer

(i) sin -1 x+ cos -1 x=(π/2), x ∈[-1,1] (ii) tan -1 x+ cot -1 x=(π/2), x ∈ R (iii) operatornamecosec-1 x+ sec -1 x=(π/2),|x| ≥ 1 Let sin -1 x=y. Then, x= sin y= cos ((π/2)-y) Therefore, cos -1 x=(π/2)-y=(π/2)- sin -1 x Hence, sin -1 x+ cos -1 x=(π/2) Similarly, we can prove the other parts.

Q. Which of the following is/are true? (i) sin−1x+cos−1x=2π​,x∈[−1,1] (ii) tan−1x+cot−1x=2π​,x∈R (iii) cosec−1x+sec−1x=2π​,∣x∣≥1

(i), (ii)

(ii), (iii)

(i), (iii)

(i), (ii), (iii)

(i) sin−1x+cos−1x=2π​,x∈[−1,1] (ii) tan−1x+cot−1x=2π​,x∈R (iii) cosec−1x+sec−1x=2π​,∣x∣≥1 Let sin−1x=y. Then, x=siny=cos(2π​−y) Therefore, cos−1x=2π​−y=2π​−sin−1x Hence, sin−1x+cos−1x=2π​ Similarly, we can prove the other parts.

Q. Which of the following is/are true?
(i) $sin^{- 1} x + cos^{- 1} x = \frac{π}{2}, x \in [- 1, 1]$
(ii) $tan^{- 1} x + cot^{- 1} x = \frac{π}{2}, x \in R$
(iii) $cosec^{- 1} x + sec^{- 1} x = \frac{π}{2}, ∣ x ∣ \geq 1$