Solving Trigonometry Equations and Problems with Examples and Tips

$\sin 2 θ + \cos 2 θ = \sin θ + \cos θ$ proof
I tried to do like this
L.H.S.
$= 2 \sin θ \cos θ + \cos^{2} θ - \sin^{2} θ$
$= \sin θ \cos θ + \cos^{2} θ + \sin θ \cos θ - \sin^{2} θ$
$= \cos θ (\sin θ + \cos θ) + \sin θ (\cos θ - \sin θ)$
Then what should I do ?

ab0utfallingm1z2 2022-03-30

$\sin^{2} x \cos^{2} x + \sin x \cos x - 1 = 0$

Addison Fuller 2022-03-30

$lim_{x \to 0} \frac{(\sin {4 x}) (- \cos {x})}{x}$ without l'Hôpital's Rule?

resaplaha7dl 2022-03-30

Proving Trig/Calc Identity $\frac{1}{1 - \sin (x)} = \frac{1 + \sin x}{{\cos (x)}^{2}}$

Jazmyn Holden 2022-03-30

Proving the identity $\frac{1}{\tan x} + \tan x = \frac{1}{\sin x \cos x}$
And here's what I've solved for:
$RHS = \frac{1}{\frac{\sin (x)}{\cos (x)}} + \frac{\sin (x)}{\cos (x)} = \frac{\cos x}{\sin x} + \frac{\sin (x)}{\cos (x)}$
Then, I get stuck. The answers section says the next step should be:
$\frac{\cos^{2} (x) + \sin^{2} (x)}{\sin (x) \cdot \cos (x)} = RHS$

sexoagotadorogyr 2022-03-30

Proving that $\sin (z + w) = \sin (w) \cos (z) + \sin (z) \cos (w)$ using complex exponentials

Rex Maxwell 2022-03-30

Proving $\tan (\frac{a + b}{2}) = \frac{\sin a + \sin b}{\cos a + \cos b}$

Harold Hoover 2022-03-30

Proving $1 + \tan^{2} (x) = \sec^{2} (x)$

svrstanojpkqx 2022-03-30

Prove trigonometric equivalence
$\sin x + \sin y = 2 \sin (\frac{x + y}{2}) \cos (\frac{x - y}{2})$

Ashleigh Shaffer 2022-03-30

Prove the identity
$\cos \frac{x}{2} \cdot \cos \frac{x}{4} \cdot \cos \frac{x}{8} = \frac{\sin x}{8 \sin \frac{x}{8}}$

plastikffxi117h 2022-03-30

Prove the inequalities
$1 - \frac{x^{2}}{2} \leq \cos (x) \leq 1 - \frac{x^{2}}{2} + \frac{x^{4}}{24}$

Aleah Choi 2022-03-30

Series $\sum_{k = 1}^{n} \frac{\tan \frac{x}{2^{k}}}{2^{k - 1} \cos \frac{x}{2^{k - 1}}}$

London Douglas 2022-03-30

Prove the following trig identities:
$2 \sin^{2} θ - 1 = \sin^{2} θ - \cos^{2} θ$
$\cos^{2} t = \sin^{2} t + 2 \cos^{2} t - 1$

ICESSRAIPCELOtblt 2022-03-30

Prove that:
$\sin (45^{\circ}) + \sin (15^{\circ}) = \sin (75^{\circ})$

Beryneingmk39 2022-03-30

Prove that,
${[\sin^{n + 1} (x)]}^{2} + {[\cos^{n + 1} (x)]}^{2} \geq {(\frac{1}{2})}^{n}$ where x is real and n is a non-negative integer.

annlanw09y 2022-03-30

Prove that $f (x) = \cos (\frac{1}{x})$ is not periodic without using calculus

Dominique Pace 2022-03-30

Prove that $\sum_{n \in N} \sin^{3} {\frac{2}{n}}$ converges

blestimd4pz 2022-03-30

Prove that $\sin (z) = \frac{e^{i z} - e^{- i z}}{2 i} = \sin (x) cosh (y) + i \cos (x) sinh (y)$
For complex z=x+iy. How to prove that
$\sin (z) = \frac{e^{i z} - e^{- i z}}{2 i} = \sin (x) cosh (y) + i \cos (x) sinh (y)$
by using the power series definition
$\sin (z) = z - \frac{z^{3}}{3!} + \frac{z^{5}}{5!} - \dots$
and Euler's formula
$e^{z} = e^{x} (\cos (y) + i \sin (y))$ ?

Rolando Wade 2022-03-30

Rearrangement inequality and minimal value of $\frac{\sin^{3} x}{\cos x} + \frac{\cos^{3} x}{\sin x}$
For $x \in (0, \frac{π}{2})$ , is the minimum value of $\frac{\sin^{3} x}{\cos x} + \frac{\cos^{3} x}{\sin x} = 1$ ? So considering $(\frac{1}{\cos x}, \frac{1}{\sin x})$ and $(\sin^{3} x, \cos^{3} x)$ is it right to use the rearrangement inequality and conclude that $\frac{\sin^{3} x}{\cos x} + \frac{\cos^{3} x}{\sin x}$ is more than or equal to $\frac{\sin^{3} x}{\sin x} + \frac{\cos^{3} x}{\cos x}$ which is equal to 1?

David Rodgers 2022-03-30

Rearranging a trigonometric expression
$\tan β = \frac{λ - \cos θ}{\sin θ} \Leftrightarrow \tan β = λ \cdot \csc θ - \cot θ$
Where $λ$ is a constant.
Is it possible to simplify the right hand side term into a single trig function? My goal is to have an equation of the form
$θ = f (β)$
Any help is appreciated.

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