Solving Trigonometry Equations and Problems with Examples and Tips

I need a hint to solve prove $\sin^{2} (6 x) - \sin^{2} (4 x) = \sin (2 x) \sin (10 x)$

Dayanara Terry 2022-07-15

Prove the identity:
$\frac{\sin x}{1 - \cos x} = \csc x + \cot x$

aangenaamyj 2022-07-15

Prove the identity:
$\frac{1}{1 - \sin x} + \frac{1}{1 + \sin x} = 2 \sec^{2} x$

invioor 2022-07-15

Prove the identity:
$\sec x - \cos x = \tan x \sin x$

cooloicons62 2022-07-15

Prove the identity:
$(\sin x + \cos x)^{2} = 1 + \sin 2 x$

mistergoneo7 2022-07-15

There exist constants $b$ , and $d$ such that
$(\sin x)^{7} = a \sin 7 x + b \sin 5 x + c \sin 3 x + d \sin x$
for all angles $x$ . Find $d$

Montenovofe 2022-07-15

Given $x, y \in (0, \frac{π}{2}]$ , $α > 0$ is a constant satisfying $0 < x + y + α < π$ ,
Also it is known that
$\frac{1}{\sin x} + \frac{1}{\sin (x + α)} = \frac{1}{\sin y} + \frac{1}{\sin (y + α)}$
How can we prove x=y "elegantly"?

cdsommegolfzp 2022-07-15

How to prove that $\csc x - 2 \cos x \cot 2 x = 2 \sin x$
$\begin{aligned} LHS \\ = & \frac{1}{\sin x} - \frac{2 \cos x}{\tan 2 x} \\ = & \frac{\tan 2 x - \sin 2 x}{\sin x \tan 2 x} \end{aligned}$
from here, I don't know how to continue

woowheedr 2022-07-15

Prove that: $\csc 50 ° + \cot 100 ° = \cot 25 ° - \csc 100 °$

Gretchen Schwartz 2022-07-15

Help with $\cos^{\frac{3}{2}} (x)$

Lucia Grimes 2022-07-15

Calculate trigonometry expression: $\frac{\cos 3 α - \sin 3 α}{\cos α + \sin α}$ if $\frac{\cos 3 α - \sin 3 α}{\cos α + \sin α}, if \sin (\frac{π}{4} - α) = 0, 1.$
I make following transformation:
$\begin{matrix} \frac{\cos 3 α - \sin 3 α}{\cos α + \sin α} = \frac{4 \cos^{3} α - 3 \cos α - 3 \sin α + 4 \sin^{3} α}{\cos α + \sin α} = \\ = \frac{4 (\cos^{3} α + \sin^{3} α) - 3 (\cos α + \sin α)}{\cos α + \sin α} = \\ = \frac{4 (\cos α + \sin α) (\cos^{2} α - \cos α \cdot \sin α + \sin^{2} α) - 3 (\cos α + \sin α)}{\cos α + \sin α} = \\ \frac{(\cos α + \sin α) [4 (1 - \sin α \cos α) - 3]}{\cos α + \sin α} = 4 - 4 \sin α \cos α - 3 = 1 - 2 \sin 2 α . \end{matrix}$
What next? How i can use substitution?

Crystal Wheeler 2022-07-15

Prove $\cos 2 α = 2 \sin^{2} β + 4 \cos (α + β) \sin α \sin β + \cos 2 (α + β)$

dream13rxs 2022-07-14

I was doing some revision and I bumped into this question.
$\cos (x) - \sec (x) = 0$ , $0^{\circ} \leq x \leq 360^{\circ}$

sebadillab0 2022-07-14

How come $\cos x \tan^{2} (x)$ can be changed to $\sec x \sin^{2} (x)$ ? What are the steps?

Donna Flynn 2022-07-14

Simplify $\sin (\frac{π}{2} - θ)$

glutynowy44 2022-07-14

If $x \in (0, \frac{π}{2})$ then find a value of x in $\frac{3}{\sqrt{2}} \sec x - \sqrt{2} \csc x = 1$

Lucia Grimes 2022-07-14

Prove: $\sin 2 θ \geq \frac{1}{2} (- 1 - 3 \cos^{2} θ)$

nidantasnu 2022-07-13

Prove the identity:
$\cos (\frac{π}{2} - x) = \sin x$

antennense 2022-07-13

Prove the identity:
$\sin (π - x) = \sin x$

uplakanimkk 2022-07-13

Find the remaining trigonometric ratios using the given value:
$\sec 0 = - 1.5, \frac{π}{2} < 0 < π$

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