All categories

4 years ago

Verify the identity. tan(θ) sin(θ) + cos(θ) = sec(θ)

Mathematics

1 answer:

MariettaO [177]4 years ago

4 0

Step-by-step explanation:

first of all

$tan = \ \frac{ \sin}{ \cos }$

put above of equation

(sin/cos)(sin)+cos =sec

sin²/cos +cos=sec

take l.c.m

sin²+cos²/cos=sec

as sin ²+cos²=1 so

1/cos=sec

sec=sec

hence proved

You might be interested in

Min knows that pi times radius equals 9.42 cm. What would she need to do to find the area?

Rus_ich [418]

$\bf \textit{area of a circle}\\\\
A=\pi r^2\\\\
-------------------------------\\\\
\textit{now, we know that }\pi r=9.42\impliedby \textit{let's square both sides}
\\\\\\
(\pi r)^2=(9.42)^2\implies (\pi ^2r^2)=9.42^2\implies \pi \pi r^2=9.42^2
\\\\\\
\stackrel{area}{\pi r^2}~~=~~\cfrac{9.42^2}{\pi }$

4 0

3 years ago

Read 2 more answers

Suppose that $x,y,z$ are positive integers satisfying $x \le y \le z$, and such that the product of all three numbers is twice t

valina [46]

The possible values of z is an illustration of the sum operator

The sum of all possible values of z is 17

<h3>How to determine the possible sum of z?</h3>

The conditions in the question are:

x <= y <= z

xyz = 2(x + y + z)

Using the trial by error method, the possible values of x, y and z are:

x = 1 , y = 3 , z = 8
x = 1 , y = 4 , z = 5
x = 2 , y = 2 , z = 4

The sum of the z values are:

z = 8 + 5 + 4

Evaluate the sum

z = 17

Hence, the sum of all possible values of z is 17

Read more about the sum operator at:

brainly.com/question/2475734

8 0

2 years ago

What are the solutions to the quadratic equation -2x^2 + 6x + 3 = 0?

mario62 [17]

For this, we will be using the quadratic formula, which is $x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$ , with a=x^2 coefficient, b=x coefficient, and c = constant. Our equation will look like this: $x=\frac{-6+/-\sqrt{6^2-4*(-2)*3}}{2*(-2)}$

Firstly, solve the multiplications and the exponents: $x=\frac{-6+/-\sqrt{36+24}}{-4}$

Next, do the addition: $x=\frac{-6+/-\sqrt{60}}{-4}$

Next, your equation will be split into two: $x=\frac{-6+\sqrt{60}}{-4},\frac{-6-\sqrt{60}}{-4}$ . Solve them separately, and your answer will be $x=-0.436,3.436$