It’s equals to 1/3 or 0.3 if you want simplified
Students who like action movies: 3/4 x 2/3 = 1/2 of the fifth grade class students
Students who like comedies: 1/2 x 4/5 = 2/5 of the fifth grade class students
You are absolutely correct
Below is the solution, I hope it helps.
<span>i) tan(70) - tan(50) = tan(60 + 10) - tan(60 - 10)
= {tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)}
ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to:
= 8*tan(10)/{1 - 3*tan²(10)}
iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10)
= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}
= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}
= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)}
= 3*tan(30) = 3*(1/√3) = √3 [Proved]
[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)},
{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]</span>
15 15 15 15 15 15 15 15 15 15