Solving Trigonometry Equations and Problems with Examples and Tips

Verify the following:
$\frac{2 \cot x}{\tan 2 x} = \csc^{2} x - 2$

Krystian Quintero 2022-02-28

It is known that
$\sqrt{9 - 8 {\sin 50}^{\circ}} = a + b {\sin c}^{\circ}$

oskrnavih92j 2022-02-28

Is there an easy way to prove the identity?
$\cos (\frac{π}{7}) - \cos (\frac{2 π}{7}) + \cos (\frac{3 π}{7}) = \cos (\frac{π}{3})$

Anniyah Povey 2022-02-28

Find the value of $α$ given
$2 \sin θ - \sqrt{5} \cos θ \equiv - 3 \cos (θ + α)$

Asiya Holder 2022-02-28

How do I prove:
$\cos (θ + 90^{\circ}) \equiv - \sin θ$

Ausanioyck 2022-02-28

Get the function value if $\sin x = \frac{2}{\sqrt{13}}$ and $\cos x = - \frac{3}{\sqrt{13}}$ and the function value is going to be calculated from $\sin (2 x - \frac{7 π}{6})$

Tagiuraoob 2022-02-28

Solve the equation:
$\int 2^{x} \tan^{9} (x^{2}) \sec (x^{2}) d x$

blakkazn924e4y 2022-02-28

Simplify the expression
$\sqrt{{(1 - \cos α \cos β)}^{2} - \sin^{2} α \sin^{2} β}$

dubinskemab 2022-02-28

How would I solve the following trig equation?
$\sin^{2} x = 1 - \cos x$

Carole Juarez 2022-02-28

Verify that
$2 \cos^{2} x - 1 = \frac{1 - \tan^{2} x}{1 + \tan^{2} x}$

Abiha Bellamy 2022-02-28

Does the equation
$a \cdot \cos (θ) - b \cdot \sin (θ) = c$
have a closed-form solution for $θ$ ?

Phoebe Xiong 2022-02-28

Given $x \geq y \geq z \geq \frac{π}{12}, x + y + z = \frac{π}{2}$ , find the maximum and minimum of $\cos x \sin y \cos z$

Cobie Sadler 2022-02-28

Prove that if $ϕ$ is not equal to $2 k π$ for any integer k, then
$\sum_{t = 0}^{n} \sin (θ + t ϕ) = \frac{\sin (n + 1) ϕ}{2}) \sin (θ + \frac{n ϕ}{2})} {\sin (\frac{ϕ}{2})}$

iristh3virusoo2 2022-02-28

How does one get the following equalities ?
$1 + \tan x = \frac{\sin (\frac{π}{4} + x)}{\cos \frac{π}{4} \cos x} = \sqrt{2} \frac{\cos (\frac{π}{4} - x)}{\cos x}$

Adrienne Rowe 2022-02-28

Help me to prove that
$\arcsin (\sqrt{2} \sin (t)) + \arcsin (\sqrt{\cos (2 t)}) = \frac{π}{2}$

Madihah Woodard 2022-02-28

How to solve the following equation?
$\tan x = \tan (x + 10^{\circ}) \tan (x + 20^{\circ}) \tan (x + 30^{\circ})$

Umaiza Hutton 2022-02-28

How can I integrate the following:
$\frac{1}{b^{2}} \int_{0}^{\infty} z^{- 2} exp (- a z) \sin^{2} (b z) d z$
for $a, b > 0$ ?

OIPLZLqm6 2022-02-28

I have given this:
$\frac{1}{8} \cot (\frac{t}{2}) \csc^{2} (\frac{t}{2}) \csc (t)$
And I have to show that it is that:
$\frac{1}{16} \csc^{4} (\frac{t}{2})$
How do I do this?

bittercynicn7f 2022-02-28

Please help me prove the identity:
$\cos^{2} a - \cos^{4} a + \sin^{4} a = \frac{1}{2} - \frac{1}{2} \cos 2 a$

fecundavai3c 2022-02-28

How can the tangent addition theorem for complex numbers
$\tan (z + w) = \frac{\tan z + \tan w}{1 - \tan z \tan w}$
be proved?

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