The expression cos⁴ θ in terms of the first power of cosine is <u>[ 3 + 2cos 2θ + cos 4θ]/8.</u>
The power-reducing formula, for cosine, is,
cos² θ = (1/2)[1 + cos 2θ].
In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.
We can do it as follows:
cos⁴ θ
= (cos² θ)²
= {(1/2)[1 + cos 2θ]}²
= (1/4)[1 + cos 2θ]²
= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}
= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)
= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]
= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8
= 3/8 + cos 2θ/4 + cos 4θ/8
= [ 3 + 2cos 2θ + cos 4θ]/8.
Thus, the expression cos⁴ θ in terms of the first power of cosine is <u>[ 3 + 2cos 2θ + cos 4θ]/8</u>.
Learn more about reducing trigonometric powers at
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Let the fist integer be x, the second is x+20
the product of the numbers is:
x(x+20)
the sum of the numbers is:
x+x+20=2x+20
the sum of the above operations will give us:
2x+20+x^2+20x=95
x^2+22x+20=95
this can be written as quadratic to be:
x^2+22x-75=0
solving the above we get:
x=3 and x=-25
but since the integers should be positive, then x=3
the second number is x+20=3+20=23
hence the numbers are:
3 and 23
a sample space, , which is the set of all possible outcomes.
A set of events , where each event is a set containing zero or more outcomes.
The assignment of probabilities to the events; that is, a function from events to probabilities.
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Answer: -1 < x < 8
x = 3
x ≠ 2
<u>Step-by-step explanation:</u>
Isolate x in the middle. Perform operations to all 3 sides.
-6 < 2x - 4 < 12
<u>+4 </u> <u> +4</u> <u>+4 </u>
-2 < 2x < 16
<u>÷2 </u> <u>÷2 </u> <u> ÷2 </u>
-1 < x < 8
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Isolate x. Solve each inequality separately. Remember to flip the sign when dividing by a negative.
4x ≤ 12 and -7x ≤ 21
<u>÷4 </u> <u>÷4 </u> <u> ÷-7 </u> <u>÷-7 </u>
x ≤ 3 and x ≥ 3
Since it is an "and" statement, x is the intersection of both inequalities.
When is x ≤ 3 and ≥ 3? <em>when x = 3</em>
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Isolate x. Solve each inequality separately.
15x > 30 or 18x < -36
<u>÷15 </u> <u> ÷15 </u> <u> ÷18 </u> <u>÷18 </u>
x > 2 or x < 2
Since it is an "or" statement, x is the union of both inequalities.
When we combine the inequalities, x is every value except 2.
x ≠ 2
Answer:
a
Step-by-step explanation:
