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Question

Solve:(tan1x)2+(cot1x)2=5π28

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Solution

(tan1x)2+(cot1x)2=5π22(tan1x)2(π2tan1x)2=5π8(tan1x)2+π24+(tan1x)2+πtan1x=5π282(tan1x)2+π45π28πtan1x=016(tan1x)28πtan1x3π2=0(4tab1x3π)(4tan1x+π)=0tan1x=3π4,tan1x=π4x=tan3π4,x=tan(π4)x=1,x=1Hence,x=1.

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