Question

If theta=30, verify, sin 3 theta = 3 sin theta - 4 sin3 theta

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Given: Ф=30

To prove: sin3Ф=3sinФ-4sin^3Ф

Solution:

Taking RHS of the expression which we have to prove

3sinФ-4sin^3Ф

put the value of Ф=30° in the place of Ф

we get the value as 3sin(30)-4sin^3(30)

we know that the value of sin30=0.5....(1)

put the value of sin30 as 0.5 in (1)

we get,

$3*0.5-4*(0.5)^{3}$

on solving we get,

sin3Ф-4sin^3Ф=1

Now taking LHS which is sin3Ф

put the value of Ф as 30° in sin3Ф

we get,

=sin3(30)

=sin90°

we know that sin90° has a value of 1

hence,

sin3Ф=1 at Ф=30°....(3)

from (2) and (3) it is clear that sin3Ф-4sin^3Ф=sin3Ф

hence proved.

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