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
Do u want us to solve if so i will do that
We know that
If the scalar product of two vectors<span> is zero, both vectors are </span><span>orthogonal
</span><span>A. (-2,5)
</span>(-2,5)*(1,5)-------> -2*1+5*5=23-----------> <span>are not orthogonal
</span><span>B. (10,-2)
</span>(10,-2)*(1,5)-------> 10*1-2*5=0-----------> are orthogonal
<span>C. (-1,-5)
</span>(-1,-5)*(1,5)-------> -1*1-5*5=-26-----------> are not orthogonal
<span>D. (-5,1)
</span>(-5,1)*(1,5)-------> -5*1+1*5=0-----------> are orthogonal
the answer is
B. (10,-2) and D. (-5,1) are orthogonal to (1,5)
£555.84
1% of the original value ×20 is £92.64. Add that to the original value (£463.20)
