Question

Please Help! Solve (sin2A)(tanA)=1 for 0º≤A≤180º.
Possible answers:
a. 45;135
b. 60;120
c. 30;150
d. 0;180

Answer 1

use the identity: \(\sf sin(2x) = 2 sin x cos x\) and \(\sf tanx=\dfrac{sinx}{cosx}\)

\(\sf (2 sin x cos x)(\dfrac{sinx}{cosx})=1\)

\(\sf (2 sin x)(sinx)=1\)

\(\sf 2 sin^2x=1\)

\(\sf sin^2x=\dfrac{1}{2}\)

\(\sf sinx=\sqrt{\dfrac{1}{2}}\)

\(\sf x=sin^{-1} (\dfrac{1}{\sqrt2})\)

use the unit circle now