Question

(1 +cos 2 theta)/(2 cos theta) = cos theta

Answer 1

Verify that is an identity...Can someone help?

Answer 2

\[\frac{ 1+\cos 2\theta }{2cos \theta } \]
=\[\frac{ 2\cos ^{2}\theta }{ 2\cos \theta } =\cos \theta \]

Answer 3

Thank You

Answer 4

\[\tan 157.5\]
Use half angle?

Answer 5

\[\tan 157.5=\tan \left( 180-22.5 \right)=-\tan 22.5\]
\[\tan 2x=\frac{ 2\tan x }{ 1-\tan ^{2}x },substitute 2x=45,\tan 2x=\tan 45=1\]
x=22.5
\[1=\frac{ 2\tan x }{ 1-\tan ^{2} x}\]
\[1-\tan ^{2}x=2\tan x\]
\[\tan ^{2}x+2\tan x -1=0 \]
\[\tan x=\frac{ -2\pm \sqrt{\left( -2 \right)^{2}-4\times1\times-1} }{2\times1 }\]
\[\tan x=\frac{ -2\pm \sqrt{4+4} }{ 2 }\]
\[\tan x=\frac{ -2\pm \sqrt{4\times2} }{ 2 }\]
\[\tan x=\frac{ -2\pm2\sqrt{2} }{ 2 }\]
\[\tan x=-1\pm \sqrt{2}\]
x=22.5 lies in first quadrant,
he\[\tan 22.5=-1+\sqrt{2}\]nce tan x is positive\[\tan 157.5=-\tan 22.5=1-\sqrt{2}\]