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Let's see

both those things in the brackets are angles.

so the question becomes sin(A+B)=sinACosB+cosAsinB

Now 

It needs to be remembered that 

the range for both inverse sine and inverse tan is    from -pi/2 to pi/2   inclusive

A=sin^-1(1/4)    so  A is in the 1st quad     sinA=1/4    and   cosA=sqrt(15 )/4

B=tan^-1(-5)     so B is in the 4th quad      tanB=-5      and   sinB=-5/sqrt(26)  and   cosB=+1/sqrt(26)

I got these ratios by drawing the right angled triangles for A and B and finig the third side use Pythagoras' theorm.

$$\\sin(A+B)\\\\
=sinACosB+cosAsinB\\\\
=\frac{1}{4}\times\frac{1}{\sqrt{26}}+\frac{\sqrt{15}}{4}\times\frac{-5}{\sqrt26}\\\\
=\frac{1}{4\sqrt{26}}+\frac{-5\sqrt{15}}{4\sqrt{26}}\\\\
=\frac{1-5\sqrt{15}}{4\sqrt{26}}\\\\
=\frac{\sqrt{26}\left(1-5\sqrt{15}\right)}{104}\\\\$$

(I have edited this a little as I made a mistake)

If you want me to explain anything just ask but think about it a bit first :)

Here are the triangles that I used.

That is wrong because you forgot to distribute the -2

cool i made this so people can let it out

3/4(x+2)=4x+5+3/2x   simplify

(3/4)x + 3/2  = 4x + 5 + (3/2)x   subtract (3/4)x from both sides

3/2 = 4x + 5 + (3/4)x     subtract 5 from both sides

3/2 - 5 = 4x + (3/4)x

3/2 - 10/2 = (19/4)x

-7/2 = (19/4)x   multiply both sides by 4/19

(-7/2)(4/19) = x  = -14/19

-50 = -2(a + 3)   divide both sides by -2

25 = a + 3          subtract 3 from both sides

22 = a

b^2-4ac is under the square root.

This is just ONE number!

2sin(2x)+ sqrt3 = 0    subtract square root 3 from both sides

2sin2x  = -√3            divide both sides by 2

sin2x = -√3 / 2

sin x  = -√3 / 2   at 240°  and  at  300°

So sin 2x = -√3 / 2   at  120° and at  150°

More general solutions are  120° + (2pi)n  and 150° + (2pi)n    where n is an integer

Product means multiplu and there is a calc on the home page :)

Thanks TayJay 

First, you would distribute -2 to both a and 3 and you would get -50=-2a-6 because you multiply -2*3 and a plus and minus equals a minus. Second, you would subtract 6 on both sides and you would get -56=-2a. Third, you would divide -2 on both sides and get 28=a and that is your answer.

Thanks taufique and welcome to the forum :)

you can also solve it by drawing up the triangle.

Then the answer might just pop out at you.  You do not need a calculator :)

42 duh

the answer is 6.8711546546790803429e51 duh. this is a calculator website you know...

sin(pi/4) = 0.707

cos^-1(sin(pi/4)) = cos^-1(0.707) = pi/4

according to Deep Thought from a hitch hikers guide to the galaxy yes 42 is the meaning of life

$$cos 30^0 =cos\frac{\pi}{6} = \sqrt3/2$$

cos is pos in the 1st and 4th quad

so

$$\\answer=2\pi n\pm\frac{\pi}{6}\qquad where\;\;n\in Z \\
$this means that n is an integer$$$

Edit

I've made a slight error here.

$$0\le cos^{-1}x \le \pi\\
$therefore the only answer is $
\dfrac{\pi}{6}$$

i know this is a joke question but the answer would be 9,867,542,309,999,999,999,999,999,999,999,013,245,769

yes, if they are parallel.

200

Actually your question really does not make sense. 

$$\\(1/3)^{x/5}=(1/9)\\
(3^{-1})^{x/5}=(1/3^2)\\
3^{-x/5}=3^{-2}\\
-x/5=-2\\
x/5=2\\
x=10$$

The answer is 2(n)+2(4).

This is using the Distibutive Property.

$$(8d^3+8d^2+3d\pm1)-1(d^3+6d^2)\\
=8d^3+8d^2+3d\pm1-d^3-6d^2\\
=8d^3-d^3+8d^2-6d^2+3d\pm1\\
=7d^3+2d^2+3d\pm1\\$$

just take the 10 remove the zero and put in the 9 so yould get 19

This means nothing to me - sorry

2^2/3^2=4/9