Question

$Statetrueorfalse$
$tan{1}^{\circ }.tan{89}^{\circ }=tan{2}^{\circ }.tan{88}^{\circ }$

• A. True
• B. False

Answer 1

The correct option is A True

$tan{1}^{\circ }.tan{89}^{\circ }=tan{1}^{\circ }.cot({90}^{\circ }-{89}^{\circ })$
$=tan{1}^{\circ }.cot{1}^{\circ }$
$=1$ $[\because tan\theta .cot\theta =1]$

Similarly,
$tan{2}^{\circ }.tan{88}^{\circ }=tan{2}^{\circ }.cot({90}^{\circ }-{88}^{\circ })$
$=tan{2}^{\circ }.cot{2}^{\circ }=1$

$\Rightarrow tan{1}^{\circ }.tan{89}^{\circ }=tan{2}^{\circ }.tan{88}^{\circ }$