Answer:
sin 3 θ = 3 sin θ - 4 sin³θ
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given sin 3 θ
= sin ( 2θ + θ )
apply trigonometric formula
<em> sin ( A + B) = sin A cos B + cos A sin B </em>
<em> sin 2 A = 2 sin A cos B</em>
<em> Cos 2 A = 1 - 2 sin² A </em>
<em> cos ² A - sin ² A = 1</em>
<u><em>Step(ii):</em></u>-
sin 3 θ = sin ( 2θ + θ )
= sin 2θ cosθ + cos2θ sin θ
= 2 sin θ cos θ cos θ +( 1 - 2 sin² θ )sin θ
= 2 sin θ (cos² θ ) + sin θ- 2 sin³ θ
= 2 sin θ ( 1- sin²θ) + sin θ- 2 sin³ θ
= 2 sin θ - 2sin³θ + sin θ- 2 sin³ θ
= 3 sin θ - 4 sin³θ
<u><em>Final answer</em></u> :-
sin 3 θ = 3 sin θ - 4 sin³θ
The LCD = 6x^2y^3 ( because LCD of 3 and 6 = 6, LCD of x^2 and x = x^2 and LCD of y and y^3 = y^3)
now divide 3x^2y into the LCD then multiply this by 5 to get the first term in the numerator and do similar process to get second term, so we get:-
5(2y^2) - 4(x)
------------------
6x^2y^3
= 2( 5y^2 - 2x)
-----------------
6x^2y^3
= 5y^2 - 2x
-----------
3x^2y^3
Answer:
120 in ³
Step-by-step explanation:
Volume is
Length x width x height
4x10x3=120
Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation. For example, 2x+4y−9 is an algebraic expression. Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.
from google