Question

if tan@=a/b,find the value of sin2@,cos2@and tan2@.(@=theta.)

Answer 1

what

Answer 2

since tan@ = sin@/cos@, sin@ = a and cos@ = b.

sin2@ = 2sin@cos@ (double angle identity), so sin2@ = 2ab.
cos2@ = (cos@)^2 - (sin@)^2 = b - a

Answer 3

sin2@=2ab(a^2+b^2)^-1
cos2@=(b-a)(a^2+b^2)^-1
tan2@=2ab(b-a)^-1

Answer 4

tan@=opposite/adjacent=a/b
so the hypothenues is sqrt{a^2+b^2}
sin@=opp/hyp=a/(sqrt{a^2+b^2})
cos@=adj/hyp=b/(sqrt{a^2+b^2})
so sin2@=2cos@sin@=2ab/(a^2+b^2)
cos2@=cos^2@-sin^2@=b^2/(a^2+b^2)-a^2/(a^2+b^2)=(b^2-a^2)/(a^2+b^2)
tan2@=sin2@/cos2@=2ab/(b^2-a^2)

Answer 5

bottom problem
this should look better

Answer 6

let me know if you have any questions shruti

Answer 7

\[\tan2@ = (2\tan@)/ (1-\tan ^{2}@)\]
\[= (2\sin@/\cos@) * 1/( 1- (\sin ^{2}/\cos ^{2})\]
\[=2sinx/cosx * (\cos ^{2}/(\cos ^{2}/\sin ^{2}))\]
\[=2sinxcosx/ (\cos ^{2} - \sin ^{2})\]
\[= 2ab / (b ^{2}-a ^{2})\]

Answer 8

remember tan means oppsite/adjacent
cos means adjacent/hyp.
sin means opposite/hyp.

Answer 9

thx

Answer 10

there is 2 problems on that attachment
to save paper i just wrote your problem on the bottom k?

Answer 11

if you like my answer click good answer :)