(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
Answer:
The height of the triangle could be found by the <u>Pythagoras theorem</u>, where the result is, with the data of the exercise:
And the area of the triangle is:
Step-by-step explanation:
When you have two measurements of a triangle, as the case in the picture, you can find the third with the <em>Pythagoras theorem</em>, which is:
As you can see in the picture, the measurement of the hypotenuse is 12, and the opposite leg could be 6, for this reason, we're gonna clear the adjacent leg of the formula above:
Now, we can replace the values in the formula obtained:
Now, as we just need the adjacent leg, we take the square root of both sides:
Now, with these data, we can find the area of the triangle with the next formula:
As the image does not contain units, it would be simply this number, however, <em>you should know that the area units are usually given squared, for example: in^2 or ft^2</em>.
Answer:
Step-by-step explanation:
Once
We have
We can proceed considering the common base of exponentials
Therefore,
