Solving Trigonometry Equations and Problems with Examples and Tips

2nd solution of $\cos x \cos 2 x \cos 3 x = \frac{1}{4}$
Attempt explained:
$(2 \cos x \cos 3 x) \cos 2 x = \frac{1}{2}$
$(\cos 4 x + \cos 2 x) \cos 2 x = \frac{1}{2}$ Let ,y=2x
$\cos^{2} y + \cos y (2 \cos^{2} y - 1) = \frac{1}{2}$

Daanish Wilcox 2022-03-01

What is derivative of
$\frac{x}{2 - \tan x}$

Reginald Owens 2022-02-28

Evaluate the integral using trigonometric substitutions.
$\int \frac{x}{\sqrt{3 - 2 x - x^{2}}} d x$

Casertowm7 2022-02-28

How Would I verify the following identity.
$\frac{(\sec A - \csc A)}{(\sec A + \csc A)} = \frac{(\tan A - 1)}{(\tan A + 1)}$

Phoebe Xiong 2022-02-28

How do you prove this identity:
$\ln | \frac{\sin x}{\cos x - 1} | = \ln | \frac{\cos x + 1}{\sin x} |$

SnuluddidaPalbx4 2022-02-28

How do I simplify the expression of
$\cos (2 x + 3 x) \cos x + \sin (3 x) \cos (\frac{x}{2} + x)$ ?

Bradlee Hooper 2022-02-28

Determine convergence of
$\sum_{n = 1}^{\infty} (\cos \frac{2}{n} - \cos \frac{4}{n})$

ennuvolat4gv 2022-02-28

How do I prove that $\sin (\frac{π}{2} + i y) = \frac{1}{2} (e^{y} + e^{- y}) = cosh y$ ?

rhita3yp 2022-02-28

How do we prove $\cos (\frac{π}{5}) - \cos (2 \frac{π}{5}) = 0.5$ without using a calculator.

kasapi0lm 2022-02-28

How to find
$\int_{\frac{π}{2}}^{\frac{π}{4}} \cot^{5} x \csc^{3} x d x$

Jasper Carlson 2022-02-28

Given $\sec^{4} θ = \frac{16}{9}$ or $\sec^{4} = \frac{{(4)}^{2}}{{(3)}^{2}}$
$\Rightarrow \sec^{2} θ = \frac{4}{3} \Rightarrow θ = \sec^{- 1} (\sqrt{\frac{4}{3}})$
hence, $θ = 2 n π \pm \frac{π}{6}$

sunyerneq 2022-02-28

I have a function in the form of:
$\cos^{- 1} (\frac{a^{2} + b x^{2}}{2 a b x}) + \cos^{- 1} (\frac{c^{2} + {d x}^{2}}{2 c d x}) = e$

Sahar Bowden 2022-02-28

I have the following type of equation which I wish to solve for t:
$\frac{x}{\cos t} - \frac{y}{\sin t} = z$

klancimarsn 2022-02-28

I need to provide a simplified version of this expression for a homework:
$\frac{\cos^{3} x - 2 \cdot \cos x + \sec x}{\cos x \cdot \sin^{2} x}$

haugmbd 2022-02-28

I am trying to solve $\sqrt{3} \tan θ = 2 \sin θ$ on the interval $[- π, π]$ .

eleticsty5 2022-02-28

How do you solve this equation for A:
$\sin (5 A) + \cos (5 A) \sin (A) - \cos (3 A) = 0$

Tomasz Gibson 2022-02-28

If $\sin x + \cos x = \frac{\sqrt{3} + 1}{2}$ then $\tan x + \cot x =$ ?

Reginald Owens 2022-02-28

My question is, how can I solve the following derivative question?
$y = \sin (\arctan x) + \tan (\arcsin x)$

OIPLZLqm6 2022-02-28

I would like to find the apothem of a regular pentagon. It follows from
$\cos \frac{2 π}{5} = \frac{- 1 + \sqrt{5}}{4}$
But how can this be proved (geometrically or trigonometrically)?

rhita3yp 2022-02-28

How can you prove that:
$\sum_{k = 1}^{n - 1} \tan^{2} \frac{k π}{2 n} = \frac{(n - 1) (2 n - 1)}{3}$
for every integer $n \geq 1$ .

The majority of Trigonometry Math problems are quite easy to solve when you have the list of answers that help you see the logic and reasoning. Looking at various examples will help you to see how certain questions are related to provided solutions.

Remember that Trigonometry requires patience and analysis. By following your analysis skills, you will help yourself find the answers. If something remains unclear, start with your exploration of examples again and go step-by-step.

Precalculus

Practice Exercises for Trigonometry