Simplify (cscxtanx)/(1+tan^2x)?
csc(x)tan(x) --------------------- 1 + tan^2(x) ...1/sin(x) * sin(x)/cos(x) =---------------------------------- ............sec^2(x) ........1/cos(x).......cos^2(x) = ------------------- x ----------- .......1/cos^2(x)......cos^2(x) = cos(x) answer//
How do you simplify tan(arcsin(x))?
tan(u) = sin(u) / cos(u) = sin(u) / sqrt(1 - sin^2(u)) whenever -pi/2 < u < pi/2. Noting that sin(arcsin(x)) = x, we get tan(arcsin(x)) = x / sqrt(1 - x^2)
Simplify sin(x) tan (x) + cos (x). It is equal to secant but I don't see how.?
tan is sin/cos giving sin^2 / cos + cos now get common denoms sin2/cos + cos2/cos sin2 + cos2 = 1 so you're left w/ 1/cos = sec
Simplify (sin(2x)-tan(x))/(cos(2x))?
replace sin(2x)=2sinxcosx tan=sin/cos and 2cos^2 (x) - 1 = cos(2x) and it'se asy to simplify
How do I simplify x= sinx^-1 (-1/3) and x= sin^-1(2)?
Think what both statments mean, you wer solving for x but reality, you have 1/3=sin(x). the idea is you want a some kind of x where taking a sin of it will give you 1/3. So rembering defentions you remember that for some value x, sin(x)=oppsite/hypotesis. We can draw a picture to help think through the problem. So you want to find missing side first, using pythagarian theorm [math] a^2+b^2=c^2,[/math] substitute, [math]a^2+1=9 [/math], [math] a^2=8[/math], [math]a=2sqrt(2)[/math]. Now you definatly know the angle you are looking for is smallest, it is not is 30, 60,90 triangle(it doesn't always work out that simple) but we are looking it is opposite of the smallest side in this case use a calculator and use similar method as you would for 30 degreesex x=30, 210, n*360+30, n*360+210 (deegrees)for n=1, 2,3,4... the reason is we are looking for all the values that satisfy the original equation. The second problem is easier if you asking about 1/2=sin(x) is for 45, 45, 90 triangle and that is even simpler. so x=n*360+45, n*360+215 for n=0,1,2,3,4....
Trig verification, simplification help!?
the general strat for these problems are all to convert the trig functions in terms of sine and cosine. 1. sec x + csc x/ tan x = 1/cos x + 1/sinx / sinx / cosx = 1/cosx + cosx/sin^2(x) = (sin^2(x )+cos^2(x ))/cosx*sin^2(x). since (sin^2(x )+cos^2(x ))=1 we have that crap being equal to 1/cosx*sin^2(x ) = secx*csc^2(x). 2. Again convert to sine and cosine: 3/sinx - 2cos^2x/sin^2x=0 3/sinx = 2cos^2x/sin^2x 3sinx/sin^2x = 2cos^2x/sin^2x (1/sin^2x) (3sinx - 2cos^2x)=0 now u either have 1/sin^2x = 0 or 3sinx-2cos^2x = 0 the first case is impossible, so 3sinx-2(1-sin^2x)=0 2sin^2x+3sinx-2=0 and solve 3. u can solve this by converting everything to sine and cosine but i'll take a shortcut and use tan^2x + 1 = sec^2x. From 3, u have tan^2x+1 = 1.5secx+1 sec^2x= 1.5secx+1 and solve as before.
Simplify to one Trig function PLEASE!![tan^(2)(x)]/[csc(x)+1...
I don't know if I understood your question... tan^2x= sin^(2)(x)/cos^(2)(x) cscx= 1/sinx Combine and get :... sin^(3)(x)/sinx+1cos(2)(x)
How does one simplify cot (arcsin(x)) without trig functions?
Start with the following facts:[math]\cot(x):=\frac{\cos(x)}{\sin(x)}[/math] for some [math]x[/math] such that [math]\sin(x)\neq 0[/math][math]\sin(\arcsin(x))=x[/math][math]\cos(x)=\sqrt{1-\sin^{2}(x)}[/math] for some [math]x[/math] such as [math]cos(x)\geq 0[/math]Putting these three facts together and rearranging, one finds:[math]\cot(\arcsin(x))=\frac{\cos(\arcsin(x))}{\sin(\arcsin(x)}=\frac{\sqrt{1-\sin^{2}(\arcsin(x))}}{x}=\frac{\sqrt{1-x^{2}}}{x}[/math] for some appropriate [math]x[/math] (left for the reader to find)Your answer is almost correct except for the denominator which should be [math]x[/math] instead.Let me know if you need more details.
How to simplify completely (no decimals please)?
cos(2x) = 2cos^2(x) - 1 Therefore: 12cos^2(45) - 6 = 6[ 2cos^2(45) - 1 ] = 6 cos(90) = 0. sin(x + y) = sin(x)cos(y) + cos(x)sin(y) Therefore: sin(65)cos(75) + cos(65)sin(75) = sin(65 + 75) = sin(140) = sin(40). sin(2x) = 2 sin(x)cos(x) Therefore: 6 sin(15)cos(15) = 3 sin(30) = 3 / 2. tan(2t) = 2tan(t) / [ 1 - tan^2(t) ] Therefore: 2tan(105) / [ 1 - tan^2(105) ] = tan(210) = tan(30) = sqrt(3) / 3.
Can someone please help me rewrite tan170*-tan110*/1+tan170*tan11... as a single trigonometric ratio?
tan 60* this is the formula for the tangent of difference of two angles, in this case 170* and 110*