Precalculus Solutions | Expert Assistance for Problems & Examples

a problem with condition $\sin (2 θ) = \tan (θ) - \cos (2 θ)$

Laura Jenkins 2022-03-02

A problem in trigonometry
If $\tan (x + y) = a + b$ and $\tan (x - y) = a - b$ Then prove that: $a \tan (x) - b \tan (y) = a^{2} - b^{2}$
I have used the formulae for $\tan (x + y)$ and $\tan (x - y)$ and then cross multiplied and then found a and b individually and then tried to put the values of a and b in " $a \tan (x) - b \tan (y)$ "(l.h.s) but it did not lead to the r.h.s.

-x-+y=1 -3x+y=7What is the solution

Milla Werner 2022-03-01

So far I got
$r = \frac{7}{4 - 2 \cos θ}$
$(r (4 - 2 \cos θ) = 7$
$r (4 - 2 (\frac{x}{r})) = 7$

Cian Orr 2022-03-01

Determine
$\sin (\frac{π}{14}) + 6 \sin^{2} (\frac{π}{14}) - 8 \sin^{4} (\frac{π}{14})$

Potherat8mi 2022-03-01

Solve the equation
$3 \sin^{2} x - 3 \cos x - 6 \sin x + 2 \sin 2 x + 3 = 0$

Brooklyn1wp 2022-03-01

Find all rational numbers p, q, r such that
$p \cos \frac{π}{7} + q \cos \frac{2 π}{7} + r \cos \frac{3 π}{7} = 1$

Ingrid Senior 2022-03-01

How do i show:
$\sin^{2} (x + y) - \sin^{2} (x - y) \equiv \sin (2 x) \sin (2 y)$

Taylor Haines 2022-03-01

I'm having trouble proving
${(\frac{\sin (\frac{n θ}{2})}{\sin (\frac{θ}{2})})}^{2} = {| \sum_{k = 1}^{| n |} e^{i k θ} |}^{2}$
where $n \in Z$ and $θ \in R$ .

Akash Matthews 2022-03-01

Does anybody know of a quick way of finding real a and b for the equation $2 \sin (x + 10) = a \sin x + b \cos x$

rhita3yp 2022-03-01

Simplify:
$\sec x \tan x (1 - \sin^{2} x)$

Ingrid Senior 2022-03-01

How can I calculate
$\sin (10^{10^{100}} - 10)$ ?

Reginald Owens 2022-03-01

How to integrate?
$\int \frac{\arctan \sqrt{x^{2} - 1}}{\sqrt{x^{2} + x}} d x$

Nyah Conrad 2022-03-01

I am being asked to prove that
$\sum_{k = 0}^{n} \cos (k x) = \frac{1}{2} + \frac{\sin (\frac{2 n + 1}{2} x)}{2 \sin (\frac{x}{2})}$

bittercynicn7f 2022-03-01

I would like to try and prove
$\frac{1 + \sin x}{\cos x} = \frac{1 + \sin x + \cos x}{1 - \sin x + \cos x}$

haciendodedorcp 2022-03-01

Find the limit
$lim_{x \to 1} \frac{(x^{2} - 1) \sin (3 x - 3)}{\cos (x^{3} - 1) \tan^{2} (x^{2} - x)}$

tumahimikgjr 2022-03-01

I have an equation that I'm trying to solve:
$\sin x + \sqrt{3} \cos x = 1$

cooopt392a0i 2022-03-01

How does this fractions simplify:
$1 + \cos 2 θ = \frac{2 - \sqrt{2}}{2}$

Jamelia Daniels 2022-03-01

Evaluate:
$\sum_{n = 1}^{m} \arctan (\frac{1}{n^{2} + n + 1})$

STATEMENT2z4 2022-03-01

Finding a for $\sin (4 a + \frac{π}{6}) = \sin (2 a + \frac{π}{5})$

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