Question

3 sin 6 degrees minus 4 cos cube 84 degrees​

Answer 1

Answer:

sin 3a =3sina -4cos^3 a

cos 3(6)=√5-1/4

Answer 2

Given,

An expression: 3 sin 6 degrees minus 4 cos cube 84 degrees

To find,

The simplified value of the given expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

For any angle x,

a) Cos (90-x)° = Sin x°

b) Sin 3x° = 3(Sin x)° - 4(Sin^3 x)°{Statement-1}

Now, on simplifying the given expression, we get;

3 sin 6 degrees minus 4 cos cube 84 degrees

= 3 Sin 6° - 4 Cos^3 84°

= 3 Sin 6° - 4 (Cos 84°)^3

= 3 Sin 6° - 4 {Cos (90-6)°}^3

= 3 (Sin 6°) - 4 (Sin 6°)^3

{according to statement-1 (a)}

= Sin (3×6)°

{according to statement-1 (b)}

= Sin 18°

= (√5-1)/4

Hence, the simplified value of the given expression is equal to (√5-1)/4.