If cos–1x sin–1x, then ______.

Question

If cos–1x > sin–1x, then ______.

KollegeApply · Accepted Answer

If cos–1x > sin–1x, then -1 $\leq$ x < $\frac{1}{2}$. Explanation: Here, given that cos–1x > sin–1x $\Rightarrow$ sin[cos^-1x] > x $\Rightarrow$ `sin[sin^-1 sqrt(1 - x^2)] > x $\Rightarrow$ sqrt(1 - x^2) > x $\Rightarrow$ x < sqrt(1 - x^2) $\Rightarrow$ x^2 < 1 - x^2 $\Rightarrow$ 2x^2 < 1 $\Rightarrow$ x^2 < $\frac{1}{2}$ $\Rightarrow$ x < +- 1/sqrt(2)` We know that – 1 $\leq$ x $\leq$ 1 So – 1 $\leq$ x < 1/sqrt(2).

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