Question

hill in the blanks:
tan 40° x tan
= 1​

Answer 1

SOLUTION

TO FILL IN THE BLANK

tan 40° x tan ___ = 1

EVALUATION

Here it is given that tan 40° x tan ___ = 1

Let the required angle = x

Then

tan 40° x tan x = 1

$\displaystyle \implies \sf{ \tan x = \frac{1}{ \tan {40}^{ \circ} } }$

$\displaystyle \implies \sf{ \tan x = \cot {40}^{ \circ} }$

$\displaystyle \implies \sf{ \tan x = \tan ( {90}^{ \circ} - {40}^{ \circ} )}$

$\displaystyle \implies \sf{ \tan x = \tan {50}^{ \circ} }$

$\displaystyle \implies \sf{ x = {50}^{ \circ} }$

FINAL ANSWER

tan 40° x tan 50° = 1

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