sec0+ten0-1/tan0+sec0+1=1+sin0/cos0

Sec0+1=Sin0+tan0/1-cos0

Cos0/sec0-tan0=1+sin0

To simplify the given expression, we need to apply the properties and identities of trigonometric functions.

Let's break down the equation step by step:

sec(0) + tan(0) - 1/tan(0) + sec(0) + 1 = 1 + sin(0)/cos(0)

Step 1: Simplify the left side of the equation.

The first step is to recall the trigonometric identities:

sec(θ) = 1/cos(θ) and tan(θ) = sin(θ)/cos(θ)

Using these identities:

(1/cos(0)) + (sin(0)/cos(0)) - 1/(sin(0)/cos(0)) + (1/cos(0)) + 1 = 1 + sin(0)/cos(0)

Now, simplify further by multiplying through by the common denominator, which is cos(0):

(cos(0)/cos(0)) + (sin(0)/cos(0))*(cos(0)/cos(0)) - (1/cos(0))*(cos(0)/sin(0)) + (1/cos(0))*(cos(0)/sin(0)) + (cos(0)/cos(0)) = (1 + sin(0))/cos(0)

This simplifies to:

1 + sin(0) - cos(0)/sin(0) + cos(0)/sin(0) + 1 = (1 + sin(0))/cos(0)

Step 2: Simplify the right side of the equation.

The right side is already in its simplified form:

(1 + sin(0))/cos(0) = (1 + sin(0))/cos(0)

Step 3: Compare both sides of the equation.

By comparing both sides, we can see that both sides are equal:

1 + sin(0) + cos(0)/sin(0) - cos(0)/sin(0) + 1 = 1 + sin(0)

Therefore, the given equation is true for any value of θ (0 in this case).

In summary, by simplifying both sides of the equation using trigonometric identities, we have shown that the equation is true for any value of θ (0 in this case).