If tan⁡ x=24/7, and 0°<x<90°, what is cos⁡(2x)?

Answer 1

tan=opposite/adjacent

draw a right triangle and find the hypotenuse

tanx=24/7

a^2+b^2=c^2

24^2+7^2=c^2

576+49=c^2

625=c^2

take the square root of both sides

c=25, the hypotenuse

sin=opposite/hypotenuse and cos=adjacent/hypotenuse

sin=24/25 and cos=7/25

cos(2x) has four different forms

here are two of them...

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

cos(2x)=1-2(24/25)^2

cos(2x)=1-2(576/625)

cos(2x)=1-1152/625

cos(2x)=1-1 527/625

cos(2x)=-527/625

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

cos(2x)=2(7/25)^2-1

cos(2x)=2(49/625)-1

cos(2x)=98/625-1

cos(2x)=98/625-625/625

cos(2x)=-527/625

you can look up the other two trig identities involving cos(2x)