cos−1x=sin‌−1x We know that the ranges of the inverse trigonometric functions limit the values of x. Specifically, for both cos−1x and sin‌−1x,x must be in the range [−1,1]. Let's denote the common value of cos−1x and sin‌−1x by θ. Therefore, we have: θ=cos−1x=sin‌−1x From the properties of inverse trigonometric functions, we know: cos‌θ=x sin‌θ=x We also know from trigonometric identities that: cos2θ+sin‌2θ=1 Substituting x into the identity, we get: x2+x2=1 2x2=1 x2=‌
1
2
x=±‌
1
√2
Since x must fall within the range [−1,1], both positive and negative values are valid within this context. However, given the problem's options, the correct answer aligns with only the positive value provided in the options list.