Question

prove that tan(45°+theta)×tan(45°-theta)=1
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Answer 1

Step-by-step explanation:

tan45+thetha=1

tan 45-theta =1

1x1=1

lhs =rhs

Answer 2

Answer:

To prove : $tan(45^\circ-\theta) \times tan(45^\circ+\theta) =1$

Now as we know

$tan(x+y)= \dfrac{tanx+ tany}{1- tanx\times tany} \text { and } tan(x-y)= \dfrac{tanx- tany}{1+ tanx\times tany}$

So we have

$\text {L.H.S } =tan(45^\circ-\theta) \times tan(45^\circ+\theta) \\\\=\dfrac{tan45^\circ- tan\theta}{1+tan45^\circ\times tan\theta} \times \dfrac{tan45^\circ+ tan\theta}{1-tan45^\circ\times tan\theta} \\\\= \dfrac{1- tan\theta}{1+1\times tan\theta} \times \dfrac{1+ tan\theta}{1-1\times tan\theta}\\\\= \dfrac{1- tan\theta}{1+tan\theta} \times \dfrac{1+ tan\theta}{1-tan\theta}=1 =\text { R.H.S }$

Hence proved