Question

plzzz.........answer with full explanation.......................................................
simplest value of-
cot 50°.cot 40°=?

Answer 1

Cot50°.cot40° = tan(90-50)×cot40° = tan40°×cot40° = tan40°×1/tan40° = 1.......hence the simplest value is 1.....

Answer 2

$\displaystyle \sf{cot \: {50}^{ \circ} . cot \: {40}^{ \circ} } = 1$

Given :

$\displaystyle \sf{cot \: {50}^{ \circ} . cot \: {40}^{ \circ} }$

To find :

The simplified value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{cot \: {50}^{ \circ} . cot \: {40}^{ \circ} }$

Step 2 of 2 :

Find simplest value of the expression

$\displaystyle \sf{cot \: {50}^{ \circ} . cot \: {40}^{ \circ} }$

$\displaystyle \sf{ = cot \: {50}^{ \circ} . cot \: ({90}^{ \circ} - {50}^{ \circ})}$

$\displaystyle \sf{ = cot \: {50}^{ \circ} . tan \: {50}^{ \circ}} \: \: \: \: \bigg[ \: \because \:cot \: ({90}^{ \circ} - \theta) = tan \: \theta\bigg]$

$\displaystyle \sf{ = \frac{1}{tan \: {50}^{ \circ}} \times tan \: {50}^{ \circ} }$

$= 1$

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