Question

if (tan theta + 2)(2 tan theta + 1) = A tan theta + B sec² theta, then AB​

Answer 1

Step-by-step explanation:

Given:-

(tan theta +2)(2 tan theta + 1) = A tan theta + B sec^2 theta

To find:-

Find the value of AB?

Solution:-

Given that:

(tan θ+ 2)(2 tan θ+ 1) = A tan θ+ B sec^2 θ

LHS:-

=>Tan θ (2 Tan θ+1) +2( 2 Tan θ+1)

=>2 Tan^2 θ+ Tan θ +4 Tan θ +2

=>2 Tan^2 θ + 5 Tan θ +2

We know that

Sec^2 θ - Tan^2 θ = 1

=>Tan^2 θ = Sec^2 θ - 1

=> 2(Sec^2 θ - 1) +5 Tan θ +2

=> 2 Sec^2 θ -2 + 5 Tan θ +2

=> 2 Sec^2 θ+ 5 Tan θ +(2-2)

=> 2 Sec^2 θ+ 5 Tan θ +0

=>2 Sec^2 θ+ 5 Tan θ

Now

2 Sec^2 θ+ 5 Tan θ = A tan θ+ B sec^2 θ

=>5 Tan θ+2Sec^2 θ =A tan θ+B sec^2 θ

On Comparing both sides then

A = 5 and B = 2

Now,

the value of AB

=>AB = 5×2

AB=10

Answer:-

The value of AB for the given problem is 10

Used formula:-

• Sec^2 θ - Tan^2 θ = 1