Step-by-step Solution

Prove the trigonometric identity $\left(1+\cos\left(x\right)+\sin\left(x\right)\right)^2=2\left(1+\cos\left(x\right)\right)\left(1+\sin\left(x\right)\right)$

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Step-by-step explanation

Problem to solve:

$\left(1+cos\left(x\right)+sin\left(x\right)\right)^2=2\left(1+cos\left(x\right)\right)\left(1+sin\left(x\right)\right)$

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Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (1+cos(x)+sin(x))^2=2(1+cos(x))*(1+sin(x)). section:I. Choose what side of the identity are we going to work on. To prove an identity, we usually begin to work on the side of the equality that seems to be more complicated, or the side that is not expressed in terms of sine and cosine. In this particular case, we will choose to work on the right side 2\left(1+\cos\left(x\right)\right)\left(1+\sin\left(x\right)\right) to reach the left side \left(1+\cos\left(x\right)+\sin\left(x\right)\right)^2. section:II. Express in terms of sine and cosine. Nothing to do in this section. Both sides of the equality are already expressed in terms of sine and cosine.

Final Answer

true

Problem Analysis

$\left(1+cos\left(x\right)+sin\left(x\right)\right)^2=2\left(1+cos\left(x\right)\right)\left(1+sin\left(x\right)\right)$

Related formulas:

1. See formulas

Time to solve it:

~ 0.06 seconds