Question

if tan theta + sec theta is equal to 2 by 3 then sec theta is ​

Answer 1

Answer:

Step-by-step explanation:

Taking x instead of theta

We have secx + tanx = 2/3-------- eqn 1

We know that sec² x - tan² x = 1

So,

(Secx - tanx)(secx + tanx)= 1

(Secx-tanx)2/3=1

Secx-tanx = 3/2-----------eqn 2

Adding eqn 1 and 2 we get

2secx = 3/2+2/3

2Secx=13/6

Secx= 13/12 answer

Answer 2

Given :

The given equation is : tanθ + secθ = 2/3

To find : The value of secθ

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will be using normal trigonometric formulas to solve this mathematical problem.

Now, we know that :

sec²θ - tan²θ = 1

(secθ + tanθ) (secθ - tanθ) = 1

(secθ + tanθ) = 1/(secθ - tanθ)

(tanθ + secθ ) = 1/(secθ - tanθ)

2/3 = 1/(secθ - tanθ)

(secθ - tanθ) = 3/2

Now,

(tanθ + secθ) + (secθ - tanθ) = (2/3) + (3/2)

2secθ = (4+9)/6

2secθ = 13/6

secθ = (13/6) × (1/2)

secθ = 13/12

(This will be considered as the final result.)

Used formula :

• sec²θ - tan²θ = 1

Hence, the value secθ is 13/12