Question

If (1+tanΘ)(1-tanΘ) = 0 , then find sin Θ + cos Θ

Answer 1

I an using A for Θ

(1+tanA)(1-tanA) = 0

1-tan²A=1                                             (because (a+b)*(a-b)=a²-b²)

1-sec²A +1=0                                       (because tan²A =sec²A-1)

-sec²A+2=0

sec²A=2

cos²A=1/2                                            (because secA=1/cosA)

cosA=1/√2

therefore A= 45 degree and sinA = 1/√2

Therefore sinA+cosA=1/√2+1/√2

=2 / (√2)

=2√2 / 2

=√2