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Question

The value of cot π4+x cot π4-x is ___________.

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Solution

cotπ4+x cotπ4-x1tan(π/4+x)×1tanπ/4-xusing identities:
tan a+b=tana+tanb1-tana tanband tana-b=tana-tanb1+tana tanb=1tanπ/4+tanx1-tanπ/4 tanx×1tanπ/4-tanx1+tanπ4 tanx=1-tanx1+tanx×1+tanx1-tanx=1
Hence, value of cotπ4+x cotπ4-x is 1.

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