can somebody help me i dont understand this question .... please
1. the possible identity cos 2x = 2 sinxcosx
A.state any non-permissible values
B.possible identity numerically
C.possible identity graphically
d prove identity
3 years ago
Answered By Emily D
Hey there, sorry it took so long for someone to answer your question! It looks like the question is saying "this MIGHT be an identity, try to prove it"
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A. NPVs happen when the value of x would make you divide something by zero OR take an even (square, 4th, 6th, etc) root a negative number. Looking at this equation, nothing is being divided or rooted, so there aren't any NPVs
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B. For this one, you're looking for a value that makes both sides equal. This is probably easiest to do by using a double-angle identity
sin(2x) = 2sin(x)cos(x)
sin(2x) = cos(2x)
So now we're looking for an angle (θ, where θ = 2x) that makes sin(θ) = cos(θ)
The only ones I can think of are π/4 and 5π/4
So 2x = π/4, which means x = π/8
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C. For this part, I think it wants you to sketch a graph of what the two equations look like and circle the intercepts.
cos(2x) = 0 at π/4, 3π/4, 5π/4, 7π/4 etc
sin(2x) = 0 at 0, π/2, π, 3π/2, etc
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D. You can't prove an identity that's untrue. I'd leave it at sin(2x) = cos(2x), say this is only true at π/8 + nπ/2, where n is an integer
3 years ago
Answered By Emily D
Hey there, sorry it took so long for someone to answer your question! It looks like the question is saying "this MIGHT be an identity, try to prove it"
-------------------
A. NPVs happen when the value of x would make you divide something by zero OR take an even (square, 4th, 6th, etc) root a negative number. Looking at this equation, nothing is being divided or rooted, so there aren't any NPVs
--------------------------
B. For this one, you're looking for a value that makes both sides equal. This is probably easiest to do by using a double-angle identity
sin(2x) = 2sin(x)cos(x)
sin(2x) = cos(2x)
So now we're looking for an angle (θ, where θ = 2x) that makes sin(θ) = cos(θ)
The only ones I can think of are π/4 and 5π/4
So 2x = π/4, which means x = π/8
--------------
C. For this part, I think it wants you to sketch a graph of what the two equations look like and circle the intercepts.
cos(2x) = 0 at π/4, 3π/4, 5π/4, 7π/4 etc
sin(2x) = 0 at 0, π/2, π, 3π/2, etc
-------------------
D. You can't prove an identity that's untrue. I'd leave it at sin(2x) = cos(2x), say this is only true at π/8 + nπ/2, where n is an integer