Harder Trig Identity Practice

Harder Trig Identity Practice

Rearrange the expressions and reasons to form a logical proof of each identity.

Put the steps in order first and check them. Once they are correct, go back to that slide, put the reasons in order, and check them. When you check one thing (steps or reasons), it will randomize the other thing, so make sure that you follow the directions or you will have extra work to do.

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$= \frac{1 - cos (x)}{cos (x)} \frac{1}{1 - cos (x)}$

$= \frac{1}{\cos (x)}$

$= \sec (x)$

$= \sec (- x)$

$\frac{\sec (x) - 1}{1 - \cos (x)}$

Prove the following trig identity: $(1 + {t a n}^{2} (θ)) {s i n}^{2} (θ) = {t a n}^{2} (θ)$

$= {s e c}^{2} (θ) {s i n}^{2} (θ)$

$= \frac{1}{{c o s}^{2} (θ)} {s i n}^{2} (θ)$

$= \frac{{s i n}^{2} (θ)}{{c o s}^{2} (θ)}$

$= {t a n}^{2} (θ)$

$(1 + {t a n}^{2} (θ)) {s i n}^{2} (θ)$

Prove the following trig identity: $2 {s e c}^{2} (α) - 2 {s e c}^{2} (α) {s i n}^{2} (α) - {s i n}^{2} (α) - {c o s}^{2} (α) = 1$

$= 2 {s e c}^{2} (α) ({1 - s i n}^{2} (α)) - ({s i n}^{2} (α) + {c o s}^{2} (α))$

$= 2 {s e c}^{2} (α) {c o s}^{2} (α) - ({s i n}^{2} (α) + {c o s}^{2} (α))$

$= 2 {s e c}^{2} (α) {c o s}^{2} (α) - 1$

$= 2 \frac{{c o s}^{2} (α)}{{c o s}^{2} (α)} - 1$

$= 2 - 1$

$= 1$

$2 {s e c}^{2} (α) - 2 {s e c}^{2} (α) {s i n}^{2} (α) - {s i n}^{2} (α) - {c o s}^{2} (α)$