Question

Q1.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

Answer:

(2) 2

Solution:

Given,

A + B = π/4

Taking “tan” on both sides,

tan(A + B) = tan π/4

(tan A + tan B)/(1 – tan A tan B) = 1

tan A + tan B = 1 – tan A tan B

tan A + tan B + tan A tan B = 1….(i)

(1 + tan A)(1 + tan B) = 1 + tan A + tan B + tan A tan B

= 1 + 1 {from (i)}

= 2

Answer 2

Step-by-step explanation:

SOLUTION

TO CHOOSE THE CORRECT OPTION

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

Then

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

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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