Which of the following is/are a rational number?

1 sin⁡(tan−1⁡3+tan−1⁡13)=sin⁡π2=12 cos⁡(π2−sin−1⁡34)=cos⁡(cos−1⁡34)=343 sin⁡(14sin−1⁡638)Let sin−1⁡638=θ.Then, sin⁡θ=638⇒cos⁡θ=18we have  cos⁡θ2=1+cos⁡θ2=34⇒ sin⁡θ4=1−cos⁡θ22=122Now, log2⁡sin⁡(14sin−1⁡638)=log2⁡122=−32(4)     cos−1⁡53=θ or cos⁡θ=53         ∴ tan⁡θ2=1−cos⁡θ1+cos⁡θ=3−52