I HAVE 5 MATH QUESTIONS AND I NEED HELP ASAP. ONLY COMMENT IF YOU'RE GONNA HELP ME PLEASE. THANKS! QUESTIONS ARE PASTED BELOW.
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Answer:
Area of trapezoidal base = 4 square units.
Step-by-step explanation:
We know that volume of a prism is known as :
where <em>B</em> is Area of Base
and <em>h</em> is Height of prism
NOTE: Formula for Volume of a prism can be generalized as above irrespective of the type of base it has (base can be of type triangle, rectangle, square or trapezoidal etc).
Here, we are given that Base is trapezoidal.
<em>h</em> is 6 units and
Volume <em>V</em> is 24 cubic units.
And we have to find out the value of B.
Putting the above values in above formula:
Hence, area of trapezoidal base = 4 square units.
(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