Question

tan32 + tan88/1-tan32*tan88

Answer 1

Answer:

it is the formula of tan (32 + 88)

because,

tan (A +B) = (tan A +tanB)/ (1- tanAtanB)

so, tan (32+88) = tan 120 = √3

Answer 2

$\displaystyle \sf{ \frac{tan \: {32}^{ \circ} + tan \: {88}^{ \circ} }{1 -tan \: {32}^{ \circ} tan \: {88}^{ \circ} } }= - \sqrt{3}$

Given :

The expression

$\displaystyle \sf{ \frac{tan \: {32}^{ \circ} + tan \: {88}^{ \circ} }{1 -tan \: {32}^{ \circ} tan \: {88}^{ \circ} } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{tan \: {32}^{ \circ} + tan \: {88}^{ \circ} }{1 -tan \: {32}^{ \circ} tan \: {88}^{ \circ} } }$

Step 2 of 2 :

Find the value of the expression

We use the formula

$\displaystyle \sf{ \frac{tan \: A + tan \: B }{1 -tan \: A \: tan \: B } = tan(A + B)}$

Take A = 32° & B = 88°

Thus we get

$\displaystyle \sf{ \frac{tan \: {32}^{ \circ} + tan \: {88}^{ \circ} }{1 -tan \: {32}^{ \circ} tan \: {88}^{ \circ} } }$

$\displaystyle \sf{ = tan \: ({32}^{ \circ} + {88}^{ \circ} ) }$

$\displaystyle \sf{ = tan \: {120}^{ \circ} }$

$\displaystyle \sf{ = - \sqrt{3} }$

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