Solution of the equation cot−1⁡x+sin−1⁡15=π4 is

We have,cot−1⁡x+sin−1⁡15=π4 ⇒tan−1⁡1x+tan−1⁡1/51−15=π4⇒tan−1⁡1x+tan−1⁡12=tan−1⁡1 ⇒tan−1⁡1x=tan−1⁡1−tan−1⁡12⇒tan−1⁡1x=tan−1⁡1−121+1⋅12⇒tan−1⁡1x=tan−1⁡13⇒x=3