Answer:
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I'm only going to alter the left hand side. The right side will stay the same the entire time
I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
So with that in mind, this is how the steps would look:
tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x
Identity is confirmed
Well there are no specific numbers, but the area of a rectangle is the length x the width, and the width is the area ÷ the length.
∠GHJ and ∠RST are complementary
⇒ ∠GHJ and ∠RST = 90°
And ∠RST and ∠ABC are supplementary
⇒ ∠RST and ∠ABC = 180°
Also, ∠GHJ = x°
⇒ ∠RST = 90° - x°
⇒ ∠ABC = 180° - ∠RST
⇒ ∠ABC = 180° - (90° - x°)
⇒ ∠ABC = 90° + x°
Answer:
There is a whole range of speeds at which you are allowed to drive, not just one. In cases like this where there is more than one correct answer, we use inequalities, not equations, to represent the situation.
Inequalities are mathematical statements that define a range of values. They are easily recognizable because they contain the symbols <, ≤,>, or ≥.
