Given that

Ayaana Buck
2021-09-09
Answered

Given that

You can still ask an expert for help

Obiajulu

Answered 2021-09-10
Author has **98** answers

Use the Pythagorean identity:

Since

asked 2021-06-16

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

asked 2020-10-18

If $\mathrm{sin}x+\mathrm{sin}y=a{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\mathrm{cos}x+\mathrm{cos}y=b$ then find $\mathrm{tan}(x-\frac{y}{2})$

asked 2021-09-14

Prove that

${\mathrm{sin}}^{2}(\frac{\pi}{8}+\frac{x}{2})-{\mathrm{sin}}^{2}(\frac{\pi}{8}-\frac{x}{2})=\frac{1}{\sqrt{2}}\mathrm{sin}x$

asked 2021-12-26

Finding all a such that $f\left(x\right)=\mathrm{sin}2x-8(a+1)\mathrm{sin}x+(4{a}^{2}+8a-14)x$ is increasing and has no critical points

Obviously, the first thing I did was to find the derivative of this function and simplify it a bit and I got:

${f}^{\prime}\left(x\right)=4({\mathrm{cos}}^{2}x-2(a+1)\mathrm{cos}x+({a}^{2}+2a-4))$

But now how do I proceed further, had it been a simple quadratic in x.

Obviously, the first thing I did was to find the derivative of this function and simplify it a bit and I got:

But now how do I proceed further, had it been a simple quadratic in x.

asked 2021-12-31

I can not find a good way to solve this rather simple-looking equation. $\mathrm{cos}x+\mathrm{cos}\sqrt{2x}=2$

I can see that 0 is a solution, but is there a good way of solving it for all the potential solutions.

I can see that 0 is a solution, but is there a good way of solving it for all the potential solutions.

asked 2021-06-13

Prove the identity

$\frac{1}{2\mathrm{csc}2x}={\mathrm{cos}}^{2}x\mathrm{tan}x$

Choose the sequence of steps below that verifies the identity

A)${\mathrm{cos}}^{2}x\mathrm{tan}x={\mathrm{cos}}^{2}x\frac{\mathrm{sin}x}{\mathrm{cos}x}=\mathrm{cos}x\mathrm{sin}x=\frac{\mathrm{sin}2x}{2}=\frac{1}{2\mathrm{csc}2x}$

B)${\mathrm{cos}}^{2}x\mathrm{tan}x={\mathrm{cos}}^{2}x\frac{\mathrm{cos}x}{\mathrm{sin}x}=\mathrm{cos}x\mathrm{sin}x=\frac{\mathrm{sin}2x}{2}=\frac{1}{2\mathrm{csc}2x}$

C)${\mathrm{cos}}^{2}x\mathrm{tan}x={\mathrm{cos}}^{2}x\frac{\mathrm{cos}x}{\mathrm{sin}x}=\mathrm{cos}x\mathrm{sin}x=2\mathrm{sin}2x=\frac{1}{2\mathrm{csc}2x}$

D)${\mathrm{cos}}^{2}x\mathrm{tan}x={\mathrm{cos}}^{2}x\frac{\mathrm{sin}x}{\mathrm{cos}x}=\mathrm{cos}x\mathrm{sin}x=2\mathrm{sin}2x=\frac{1}{2\mathrm{csc}2x}$

Choose the sequence of steps below that verifies the identity

A)

B)

C)

D)

asked 2022-09-05

Solve the identy. $\frac{1+\mathrm{sin}2x}{\mathrm{cos}x+\mathrm{sin}x}=\frac{\mathrm{cos}2x}{\mathrm{cos}x-\mathrm{sin}x}$