The task is to prove the trigonometric identity that tan(x1+x2) = (tan(x1) + tan(x2)) / (1 - tan(x1)tan(x2)). This involves using the sum of angles formula for tangent and manipulating the expression to show that the left-hand side is equal to the right-hand side. By simplifying both sides of the equation and showing that they are equal, we can confirm that the identity is correct. **

Yes, it is possible to get a tan while wearing makeup, but the makeup may act as a barrier and inhibit the tanning process. Some makeup products contain SPF which can block the sun's rays and prevent tanning. It is recommended to remove makeup before sun exposure to ensure an even tan and to allow the skin to properly absorb sunlight. Additionally, prolonged sun exposure can be harmful to the skin, so it is important to wear sunscreen even if you are not tanning. **

To prove that tan(x1+x2) = (tan(x1) + tan(x2)) / (1 - tan(x1)tan(x2)) is correct, one would need to use trigonometric identities such as the sum-to-product formula and the tangent addition formula. By manipulating the expressions using these identities, one can show that both sides of the equation are equivalent. It is important to carefully follow the steps of the proof and ensure that each manipulation is mathematically sound in order to confirm the correctness of the statement. **

To show that the equation tan(x1+x2) = (tan(x1) + tan(x2)) / (1 - tan(x1)tan(x2)) is correct, we can start by using the sum formula for tangent, which states that tan(x1+x2) = (tan(x1) + tan(x2)) / (1 - tan(x1)tan(x2)). We can then substitute the values of tan(x1) and tan(x2) into the equation and simplify both sides to see if they are equal. Finally, we can verify the result by checking if both sides of the equation are equal for different values of x1 and x2. **

Yes, you can still get a tan while wearing makeup. However, the makeup may create a barrier that can reduce the amount of UV rays that reach your skin, potentially slowing down the tanning process. It's important to note that wearing makeup does not provide significant sun protection, so it's still important to use sunscreen to protect your skin from sun damage. Additionally, it's important to reapply sunscreen throughout the day, especially if you're spending extended periods of time in the sun. **

Yes, you can still get a tan while wearing makeup. However, the makeup may act as a barrier and reduce the amount of sun exposure your skin receives, potentially resulting in a lighter tan. It is important to wear sunscreen underneath your makeup to protect your skin from harmful UV rays and prevent sun damage. **

Yes, it is possible to distinguish a natural tan from a tanning bed tan. A natural tan tends to be more gradual and even, often developing over time with exposure to the sun. On the other hand, a tanning bed tan can appear more sudden and may have a more uniform color due to the concentrated UV exposure. Additionally, tanning bed tans may have a slightly different tone or hue compared to a natural tan. **

Mobile TAN (mTAN) and Smart TAN are both methods of generating one-time passwords for online banking transactions. The main difference between the two is the method of receiving the TAN. With Mobile TAN, the one-time password is sent to the user's mobile phone via SMS. On the other hand, Smart TAN uses a dedicated device, often a small card reader or a smartphone app, to generate the TAN. While Mobile TAN relies on the user's mobile phone and network coverage, Smart TAN requires the use of a separate device, providing an extra layer of security. **