I'm confused, I get dy/dx= √3sec²x/√1-3tan²x. How can it be further simplified?
#Derivatives
idle nova
glacial jasperBOT
I'm confused, I get dy/dx= √3sec²x/√1-3tan²x. How can it be further simplified?
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idle nova
1-cos3x/cos³x= cos³x-4cos³x+3cosx/cos³x = 3sec²x-3 = 3(tan²x)
Rooting it would make it √3 tanx
sin-1√3 tanx = √3sec²x/√1-3tan²x
but there's no option showing it
And if I further simplify it, it becomes at most
√3sec²x/√(3(cos²x-sin²x)/3cos²x)= √3secx/√cos2x
Yet no options resemble it
torpid hawk
I'm confused, I get dy/dx= √3sec²x/√1-3tan²x. How can it be further simplified?
What they want you to do here is take sine of both sides first. Then:
sin(y) = √(1 - cos(3x)/cos(x)^3)
Then, as cos(3x) = 4cos(x)^3 - 3cos(x):
sin(y) = √(1 - 4 + 3/cos(x)^2)
You can do the rest.