1. assalamu'alaikum.... kak mohon bantuannya... matematika tentang trigonometri..... no 1,2,3,4,5,6.... Question from @riorocker10

October 2018 1 100 Report

1. assalamu'alaikum.... kak mohon bantuannya... matematika tentang trigonometri.....
no 1,2,3,4,5,6,7,8,10,11,12,13.

fatihahalhusna Nomor 1 A
cos 17 = sin 73
$\cos^217^0-\sin^273^0=0$

Nomor 2 (???)

$\displaystyle \frac{x\csc^230\sec^245}{8\cos^245\sin^260}=\tan^260-\tan^230\\\\\frac{x(4)(2)}{8(\frac{1}{2})(\frac{3}{4})}=\frac{3}{4}-\frac{1}{3}\\\\\frac{x}{(\frac{1}{2})(\frac{3}{4})}=\frac{3}{4}-\frac{1}{3}\\x=\frac{15}{96}$ (?)

Nomor 3 (C)

Nomor 4 (???)

$\sin(2x-30)=-\cos(3x+50)\\-\cos(-2x+120)=-\cos(3x+50)\\-2x+120=3x+50\\x=14$

Nomor 5 (???)

$\tan(2x+60)=\cot(90-3x)\\2x+60=-3x\\5x=-60\\x=-12$

Nomor 6 (C)

$\displaystyle \sqrt{\frac{1-\sin x}{1+\sin x}}=\sqrt{\frac{(1-\sin x)^2}{\cos^2 x}}\\\\=\sec x-\tan x$

Nomor 7 (????)
$x^2=\cot^2\alpha+2\cot\alpha\cos\alpha+\cos^2\alpha\\y^2=\cot^2\alpha-2\cot\alpha\cos\alpha+\cos^2\alpha\\\\x^2-y^2=4\cot\alpha\cos\alpha$

Nomor 8 (A)

$x^2+y^=r^2\{\sin^2A\cos^2B+\sin^2A\sin^2B\}=r^2\sin^2A\\\\x^2+y^2+z^2=r^2\sin^2A+r^2\cos^A\\\\x^2+y^2+z^2=r^2$

Nomor 10 (C)
$\cos x+\sin x=\sqrt{2}\cos x\rightarrow 1+2\cos x\sin x=2cos^2x\\\cos x-\sin x=K\rightarrow ~~~~~~~~1-2\cos x\sin x=K^2\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~------------~~~~+\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2=K^2+2\cos^2 x\\\\K^2=2(1-\cos^2 x)\\K=\sqrt{2}\sin x$

Nomor 11 (D)
$\displaystyle \frac{(\cot\theta\tan\theta-\cot\theta\tan3\theta)-(\cot\theta\tan\theta-\cot3\theta\tan\theta)}{\cot\theta\tan\theta-\cot\theta\tan3\theta-\cot3\theta\tan\theta+\cot3\theta\tan3\theta}\\\\=\frac{2-\cot\theta\tan3\theta-\cot3\theta\tan\theta}{2-\cot\theta\tan3\theta-\cot3\theta\tan\theta}=1$

Nomor 12
$(\sin^2x-\cos^2x)(\sin^2x+\cos^2x)-2\sin^2x\\=\sin^2x-\cos^2x-2\sin^2x\\=-\sin^2x-\cos^2x\\=-1$