Question

If A=pi/4then (1+tan A) (1+tan ^2 A) (1+tan^3 A) =
1) 6 2) 4 3) 8 4)2​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If $\displaystyle \sf{A = \frac{\pi}{4} }$

Then

$\displaystyle \sf{(1 + { \tan}^{} A )(1 + { \tan}^{2} A )(1 + { \tan}^{3} A )}$

1) 6

2) 4

3) 8

4) 2

EVALUATION

Here it is given that

Now the given expression

$\displaystyle \sf{ = (1 + { \tan}^{} A )(1 + { \tan}^{2} A )(1 + { \tan}^{3} A ) }$

$\displaystyle \sf{ = (1 + { \tan}^{} \frac{\pi}{4} )(1 + { \tan}^{2} \frac{\pi}{4} )(1 + { \tan}^{3} \frac{\pi}{4} )}$

$\displaystyle \sf{ = (1 + 1 )(1 + 1 )(1 + 1)}$

$= 2 \times 2 \times 2$

$= 8$

FINAL ANSWER

Hence the correct option is 3) 8

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Answer 2

Step-by-step explanation:

SOLUTION

TO CHOOSE THE CORRECT OPTION

If

\displaystyle \sf{A = \frac{\pi}{4} }A=

4

π

Then

\displaystyle \sf{(1 + { \tan}^{} A )(1 + { \tan}^{2} A )(1 + { \tan}^{3} A )}(1+tan

A)(1+tan

2

A)(1+tan

3

A)

EVALUATION

Here it is given that

Now the given expression

\displaystyle \sf{ = (1 + { \tan}^{} A )(1 + { \tan}^{2} A )(1 + { \tan}^{3} A ) }=(1+tan

A)(1+tan

2

A)(1+tan

3

A)

\displaystyle \sf{ = (1 + { \tan}^{} \frac{\pi}{4} )(1 + { \tan}^{2} \frac{\pi}{4} )(1 + { \tan}^{3} \frac{\pi}{4} )}=(1+tan

4

π

)(1+tan

2

4

π

)(1+tan

3

4

π

)

\displaystyle \sf{ = (1 + 1 )(1 + 1 )(1 + 1)}=(1+1)(1+1)(1+1)

= 2 \times 2 \times 2=2×2×2

= 8=8