Web Analytics

Verified Answer :

syed514

sinx=1/3

secy=1/cosy=5/4 => cosy=4/5

cos(x+y)=cosxcosy-sinxsiny
=cosx(4/5)-(1/3)siny

so now we need to know cosx and siny
i drew two triangles
one where sinx=1/3=20/(320)

one where cosx=4/5=124/(125)
 i got the following conclusion: sin(y)=36/60=3/5
and cosx=40(2)^(1/2)/60=2(2)^(1/2)/3

so we have
cos(x+y)=2sqrt(2)/3 4/5 -1/3 * 3/5 = 8sqrt(2) -3 /15 

HomertheGenius

cos x = √(1-1/9) = √8/9 = 2√2/3
sin y = √( 1 - 16/25) = √9/25 = 3/5
Additional formula:
cos ( x + y ) = cos x cos y - sin x sin y =
\(= \frac{2 \sqrt{2} }{3}* \frac{4}{5}- \frac{1}{3}* \frac{3}{5}= \\ \frac{8 \sqrt{2} }{15}- \frac{3}{15}= \frac{8 \sqrt{2}-3 }{15}\)

Related Questions