Question

If Tan 8A – Tan 5A–Tan 3A = K Tan 8A Tan 5A.Tan 3A then K =

a) 3 b) 2 c) 1 d) 4

Answer the option ​

Answer 1

Answer:

K = 1

Step-by-step explanation:

Given,

tan8A - tan5A - tan3A = $K\times tan8A\times tan5A\times tan3A$

To Find :-

Value of 'k'.

Solution :-

Taking L.H.S :-

tan8A - tan5A - tan3A

= tan8A - (tan5A + tan3A)

[Let it be equation -- (1)]

We can write , 8A = 5A + 3A

Applying "tan" on both sides :-

tan(8A) = tan(5A + 3A)

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

$tan8A=\dfrac{tan5A+tan3A}{1-tan5Atan3A}$

$tan5A+tan3A=tan8A(1-tan5A tan3A)$

[--- Let it be equation (2)]

Substituting value of equation 2 in value of equation 1 :-

$=tan8A-(tan8A(1-tan5A tan3A))$

= tan8A - (tan8A - tan8Atan5Atan3A)

= tan8A - tan8A + tan8Atan5Atan3A

= tan8Atan5Atan3A

= $1\times tan8Atan5Atan3A$

Since Comparing R.H.S and above equation :-

We can say that 'K' = 1

Hence option 'C'  K = 1

Answer 2

Answer:

answer = 1

Step-by-step explanation:

=

1−tan5A⋅tan3A

tan5A+tan3A

tan8A(1−tan5A⋅tan3A)=tan5A+tan3A

+tan5Atan3Atan8A=tan8A−tan5A−tan3A

on comparing, we get K=1

hence, (C) is the correct option.