Question

If sec theta -tan theta =1/3 then find the value of sec theta + tan theta.

Answer 1

Answer:

answer is 3

Step-by-step explanation:

it so simple that

sec theta - tan theta = 1/k ,

where k is some constant value,then

sec theta + tan theta = k

like wise sec theta - tan theta = 1/3 then

sec theta + tan theta = 3

Answer 2

Given:

A trigonometric equation sec(theta) - tan(theta) = 1/3.

To Find:

The value of sec(theta) + tan(theta) is?

Solution:

The given problem can be solved using trigonometric identities.

1. The trigonometric identity used to solve the given problem is,

• sec²(x) - tan²(x) = 1

2. The algebraic identity used to solve the given problem is,

• a² - b² = (a+b)(a-b)

3. The value of sec(theta) - tan(theta) = 1/3,

=> Consider the trigonometric identity mentioned in the point 1,

=> sec²(theta) - tan²(theta) = 1,

=> It can be factorized using the algebraic identity mentioned above,

=> [sec(theta) + tan(theta)] x [sec(theta) + tan(theta)]= 1,

=> Substitute the value of [sec(theta) - tan(theta)] as 1/3,

=> [sec(theta) + tan(theta)] x (1/3) = 1, ( simplify the equation ),

=> [sec(theta) + tan(theta)]  = 3 x 1,

=> [sec(theta) + tan(theta)] = 3.

Therefore, the value of sec(theta) + tan(theta) is 3.