Question

if A=30°,prove sin3A=3sinA-4sin౩A

Answer 1

L.h.s ......sin3a=sin90°=1.
R.h.s....3sina-4sin^3a=3sin30°-4(sin30°)^3=(3/2)-4(1/2)^3=1.5-0.5=1
l.h.s=r.h.s (Proved)

Answer 2

Given,

A = 30°

To prove,

Sin 3A = 3Sin A-4 Sin³A

Solution,

We can easily solve this problem by following the given steps.

According to the question,

A = 30°

Now, putting the value of A in Sin 3A = 3Sin A-4 Sin³A,

[Note that Sin³A can be re-written as (Sin A)³.]

Sin (3×30) = 3Sin 30 -4(Sin 30)³

Sin 90 = 3Sin 30-4 (Sin 30)³

Putting the value of Sin 90 to be 1 and that of Sin 30 to be 1/2,

1 = 3×1/2 - 4×(1/2)³

1 = 3/2 -4×1/8

1 = 3/2-1/2

Taking the LCM to be 2 and subtracting the fractions,

1 = (3-1)/2

1 = 2/2

1 = 1

Left Hand Side (LHS) = Right-hand side (RHS)

Hence, this is proved that Sin 3A = 3Sin A-4 Sin³A.