Question

If log_sinx(cosx)=1/2, and 0 12 years ago

Answer 1

lets apply the definition,

\(\log_ab=c \implies b=a^c\)

you knew this, right ?

Answer 2

what will
log_sinx(cosx)=1/2
simplify to ?

Answer 3

Sinx^1/2=cosx?

Answer 4

yup, now square both sides

Answer 5

Sinx= (cosx)^2

Answer 6

try to bring everything in sin x

Answer 7

how would u write cos^2 x in terms of sin x ?

Answer 8

cos( 2x) = 1 - sin^2( x)

Answer 9

you meant cos^2x = 1-sin^2 x
then its correct :)
so
sin x = 1-sin^2 x

can you now solve for sin x ? its just a quadratic

Answer 10

still here ? stuck or trying ?

Answer 11

Sin^2x+sinx -1=0 is this right?

Answer 12

yup.
its like
y^2 + y-1 =0
where y= sin x
a simple quadratic equation, solve for y, you would have solved for sin x