Solution of the equation tan⁡cos−1⁡x=sin⁡cot−1⁡12 is

We have, tan⁡cos−1⁡x=sin⁡cot−1⁡12⇒tan⁡tan−1⁡1−x2x=sin⁡tan−1⁡2⇒tan⁡tan−1⁡1−x2x=sin⁡sin−1⁡21+4⇒tan⁡tan−1⁡1−x2x=sin⁡sin−1⁡25⇒1−x2x=25⇒51−x2=4x2⇒9x2=5,∴x=±53.