How do you simplify this?

Mathematics

1 answer:

levacccp [35]2 years ago

4 0

Answer:

tan x

Step-by-step explanation:

(tan-x)[sec(pi/2)-x] (sin-x)

We know that tan (-x) = - tan (x) and sin (-x) = - sin (x)

-(tanx)[sec(pi/2)-x] -(sinx)

(tanx)[sec(pi/2)-x] (sinx)

Using the identity sec = 1/ cos

sec ( pi/2 -x) =1/cos ( pi /2 -x)

We know that cos (s-t)=cos (s) cos(t) + sin (s) sin (t)

1/ ( cos pi/2 cos x + sin pi/2 sin x) = 1/(0 cos x - 1 sinx) = 1 / sinx

Replacing into the equation

(tanx)[1/ sinx] (sinx)

tan x

You might be interested in

Which of the following statements is the most precise and correct to define an angle?

iragen [17]

Answer:

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$