Question

show that tan(45+A) tan(45-A) = 1​

Answer 1

Answer:

Step-by-step explanation:

Since, 1) tan(A+B)= (tan A + tan B)/ (1 - tanA.tanB)

          2) tan(A-B)= (tan A - tan B)/ (1 + tan A tan B)

tan(45-A)= tan45 +tan A / 1- tan45 tanA

             =1 + tanA/1- tanA

tan(45-A)= tan45-tanA/1+ tan45 tanA

=1-tanA/ 1+tanA

tan(45+A)tan(45-A)

=1+tanA/1-tanA ×1-tanA/1+tanA

=1+tanA/1+tanA × 1-tanA/1- tanA

= 1×1

=1

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