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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Cube has 6 faces/planes :)
The answer is 800.
To find this, multiply 10 times 8 to find the number you are dividing. (80) now, multiply 80 by 10. (800)
1/10 of 800 is 80, which is ten times as much as 8.
Answer:
4Q a). angle1=55°
angle2=23°
angle3=63°
angle4=125°
5Q. x=35°
6Q. y=15°
8Q. C. 28°
9Q. Yes, they are congruent by S.S.S. congruence
10Q. A.A.S.
11Q. S.S.S.
12Q. Not possible
13Q. S.A.S.
14Q. S.S.S.
15Q. 66°
16Q. 24°
I hope it will be useful.
Step-by-step explanation:
7Q. angle1=angle3 (Alternate Interior Angles)
angle2=angle4 (A.I.A.)
angleXWZ=angleXYZ (opposite angles of a parallelogram)
By A.A.A. congruence criteria, they are congruent.
8Q. Hint: Make the diagram first!
AngleC is halved since M is the mid-point.
angleA=angleB (Property of an isosceles triangle)
which implies, angleAMC=angleBMC=90°
Thus, CM is perpendicular to AB.
I hope it will be useful.
