Question

prove that cot theta ÷ 1 - cot theta + tan theta ÷ 1-tan theta = -1​

Answer 1

heya buddy here is your answer

so for answering your question in a better way i assume that theta=A

so

[cotA/(1-cotA)]+[tanA/(1-tanA)]

TAKING LCM AS (1-cotA)(1-tanA)

then [cotA(1-tanA)+tanA(1-cotA)]/(1-cotA)(1-tanA)

=[cotA-1+tanA-1]/[1-tanA-cotA+1]                      {as tanA*cotA=1}

=cotA+tanA-2/2-tanA-cotA

=-(2-tanA-cotA)/2-tanA-cotA

=-1

hence proved

hope it helps buddy

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