Derive the prism formula. Show that
(i) `n = frac(sin(frac(A + delta_m)(2)))(sin(frac(A)(2))`

If the measured values of two quantities are A +- Delta A and B +- Delta B , and Delta A and Delta B being the mean absolute errors. What is the maximum possible error in A + B ? Show that if Z=frac(A)(B) then frac (Delta Z)(Z) = frac (Delta A)(A) + frac (Delta B)(B)

Show that 2sin^-1(frac{3}{5}) = tan^-1(frac{24}{7})

Show that tan^-1(frac{1}{2})-tan^-1(frac{1}{4}) = tan^-1(frac{2}{9})

Prove the following: (frac(sin(A-B))(cosAcosB))+(frac(sin(B-C))(cosBcosC))+(frac(sin(C-A))(cosCcosA))=0

Prove the following: frac(sin(x+y))(sin(x-y))=frac(tanx+tany)(tanx-tany)

Prove the following: (frac(sin3x)(cosx))+(frac(cos3x)(sinx))=2cot2x

Prove the following: (frac(sin2x+sin2y)(sin2x-sin2y))=(frac(tan(x+y))(tan(x-y)))

Evaluate: int frac {sin 2x}{cos x} dx

Evaluate the following: int frac{sin x}{sin 3x} dx

Solve the following: In /_\ABC prove that cos(frac{A-B}{2}) = frac{a+b}{c}sin(frac{C}{2})