Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
Answer: it's a linear equation
Step-by-step explanation:
Answer:
71°
Step-by-step explanation:
31-3x+19x-5=90
16x=90-26
16x=64
x=4
m<R=19x-5 = 19(4)-5 = 76-5 = 71
Improper fractions are called such because the numerator is greater than the denominator. The only way it can be simplified is through a mixed fraction.
c) 10/3 is the improper fraction.
10/3 is simplified into 3 1/3.
Answer:
Step-by-step explanation:
Let the ages be r and m
<u>We have:</u>
<u>Substitute m in the second equation and solve for r:</u>
- m = 117 - r
- 5r = 9 + 3( 117 - r)
- 5r = 9 + 351 - 3r
- 5r + 3r = 360
- 8r = 360
- r = 360/8
- r = 45
<u>Then m is</u>
