Question

If if M is equal to 10 theta plus sin theta and N is equal to tan theta minus sign theta then prove that M square minus N square whole square is equal to 16mn

Answer 1

Answer:

m = tan∅+sin∅

n = tan∅-sin∅

⇒m+n = 2 tan∅ & m-n = 2 sin∅

⇒$m^{2}$-$n^{2}$ = 4 tan∅ sin∅

squaring both sides

($m^{2}$-$n^{2}$)^2 = 16 tan^2∅ Sin^2∅......................(A)

⇒$m^{2}$+$n^{2}$ +2 mn= 4 tan^2∅ .............1

⇒$m^{2}$+$n^{2}$ -2 mn= 4 sin^2∅.............2

subtract 2 from 1

4 mn = 4(tan ^2∅-Sin^2∅)

4 mn = 4 sin^2∅(1- cos^2∅)/cos^2∅

4mn = 4 sin^2∅.Sin^2∅/cos^2∅

4mn = 4 tan^2∅.Sin^2∅

mn = tan^2∅.Sin^2∅...................(B)

put B in A

we have LHS = RHS