Simplify the trigonometric expression (1+tan(x))^2-tan(x)

 Exercise

$\left(1+\tan\left(x\right)\right)^2-\tan\left(x\right)$

 

Expand the expression $\left(1+\tan\left(x\right)\right)^2$ using the square of a binomial: $(a+b)^2=a^2+2ab+b^2$

$1+2\tan\left(x\right)+\tan\left(x\right)^{2}-\tan\left(x\right)$

 

Combining like terms $2\tan\left(x\right)$ and $-\tan\left(x\right)$

$1+\tan\left(x\right)+\tan\left(x\right)^{2}$

 

Applying the trigonometric identity: $1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2$

$\sec\left(x\right)^2+\tan\left(x\right)$

 Why is tan(x)^2+1 = sec(x)^2 ?

$\sec\left(x\right)^2+\tan\left(x\right)$

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