How do you solve for x if $cos (6 x - 20) = sin (2 x - 10)$ $cos (6x-20) = sin (2x - 10)$ ?

Question

How do you solve for x if $cos (6 x - 20) = sin (2 x - 10)$ $cos (6x-20) = sin (2x - 10)$ ?

1 Answer

Impact of this question

5523 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-24T02:30:19

$x = 15$ $x=15$

Explanation:

$sin x = cos (90 - x)$ $sin x =cos (90-x)$
$cos x = sin (90 - x)$ $cosx = sin (90-x)$

$cos (6 x - 20) = sin (90 - (6 x - 20)) = sin (90 - 6 x + 20) = sin (110 - 6 x)$ $cos (6x-20)=sin(90-(6x-20))=sin(90-6x+20)=sin(110-6x)$

$sin (110 - 6 x) = sin (2 x - 10)$ $sin(110-6x)=sin(2x-10)$

$110 - 6 x = 2 x - 10$ $110-6x=2x-10$

$120 = 8 x$ $120=8x$

$x = 15$ $x=15$

Sub $x = 15$ $x=15$ into the equation
LHS:
$cos (6 x - 20)$ $cos(6x-20)$
$= cos (6 \times 15 - 20)$ $=cos(6times15-20)$
$= cos (90 - 20)$ $=cos(90-20)$
$= cos 70$ $=cos70$

RHS:
$sin (2 x - 10)$ $sin(2x-10)$
$= sin (2 \times 15 - 10)$ $=sin(2times15-10)$
$= sin (30 - 10)$ $=sin(30-10)$
$= sin 20$ $=sin20$
$= cos (90 - 20)$ $=cos(90-20)$
$= cos 70$ $=cos70$
$= L H S$ $=LHS$

Therefore, $x = 15$ $x=15$ is correct

Science

Math

Humanities

... and beyond

How do you solve for x if $cos (6 x - 20) = sin (2 x - 10)$ $cos (6x-20) = sin (2x - 10)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve for x if cos (6x-20) = sin (2x - 10)cos(6x−20)=sin(2x−10)cos (6x-20) = sin (2x - 10)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve for x if $cos (6 x - 20) = sin (2 x - 10)$ $cos (6x-20) = sin (2x - 10)$ ?