Statement-I: If displaystyle∑ i =12 n displaystyle sin -1 x 1= n π, n ∈ N. Then displaystyle∑ i =1 n x i = displaystyle∑ i =1 n x 12= displaystyle∑ i =1 n x 13 Because Statement-II: -(π/2) ≤ sin -1 x ≤ (π/2), ∀ x ∈[-1,1]

Question

Statement-I: If displaystyle∑ i =12 n displaystyle sin -1 x 1= n π, n ∈ N. Then displaystyle∑ i =1 n x i = displaystyle∑ i =1 n x 12= displaystyle∑ i =1 n x 13 Because Statement-II: -(π/2) ≤ sin -1 x ≤ (π/2), ∀ x ∈[-1,1] (A) Statement-I is true, Statement-II is true; Statement-II is correct explanation for Statement-I. (B) Statement-I is true, Statement-II is true; Statement-II is NOT a correct explanation for statement-I. (C) Statement-I is true, Statement-II is false. (D) Statement-I is false, Statement-II is true.

Tardigrade Admin · Accepted Answer

Correct answer is (a) Statement-I is true, Statement-II is true; Statement-II is correct explanation for Statement-I.

Q. Statement-I : If i=1∑2n​sin−1x1​=nπ,n∈N. Then i=1∑n​xi​=i=1∑n​x12​=i=1∑n​x13​ Because Statement-II : −2π​≤sin−1x≤2π​,∀x∈[−1,1]

Statement-I is true, Statement-II is true; Statement-II is correct explanation for Statement-I.

Statement-I is true, Statement-II is true; Statement-II is NOT a correct explanation for statement-I.

Statement-I is true, Statement-II is false.

Statement-I is false, Statement-II is true.

Correct answer is (a) Statement-I is true, Statement-II is true; Statement-II is correct explanation for Statement-I.

Q. Statement-I : If $i = 1 \sum 2 n sin^{- 1} x_{1} = nπ, n \in N$ . Then $i = 1 \sum n x_{i} = i = 1 \sum n x_{1}^{2} = i = 1 \sum n x_{1}^{3}$ Because
Statement-II : $- \frac{π}{2} \leq sin^{- 1} x \leq \frac{π}{2}, \forall x \in [- 1, 1]$