(tanθ + cotθ)² = sec²θ + csc²θ
<u>Expand left side</u>: tan²θ + 2tanθcotθ + cot²θ
<u>Evaluate middle term</u>: 2tanθcotθ = = 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
<u>Apply trig identity:</u> tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
<u>Apply trig identity:</u> 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
<em>c = 10</em>
Step-by-step explanation:
We can find out the missing side of a right triangle by using the Pythagorean theorem.
The Pythagorean theorem is...
We can even double check the first problem by plugging in everything into the theorem and solving, everything will come out correct. We can plug in the numbers from the second problem into the theorem and find c, also please note that the hypotenuse of a triangle will <em>always </em>be c. It doesn't matter which you put in for a or b, but since the problem gives us which one is a and which one is b, I'll just be plugging it in like that.
A lot of people will stop here and think that the answer is 100, but you need to find the square root of 100, since c is squared. The square root of 100 is 10, so...
<em><u>c = 10</u></em>