From the equation of motion, we know,
Where s= displacement
u= initial velocity
a= gravitational force
t= time
Displacement is 0 since the ball comes back to the same point from where it was thrown.
A = 
since the ball is thrown upwards.
Plug the known values into the equation.
=> 
Solving for u gives :
u= 16.67 m/ sec ....... equation (1)
At maximum height, final velocity i.e v is 0
Time take to reach the top = 
=> 
Solving for s we get
s= 14.16 m
A loss in 2 points per forget, times 6 times forgetting gives 12. But since it is a deduction in points the final integer answer is -12
Answer:
Verified below
Step-by-step explanation:
We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)
In trigonometric identities;
Cot θ = cos θ/sin θ
Thus;
(cot θ - 1)/(cot θ + 1) gives;
((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)
Simplifying numerator and denominator gives;
((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)
This reduces to;
>> (cos θ - sin θ)/(cos θ + sin θ)
Multiply top and bottom by ((cos θ + sin θ) to get;
>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)
In trigonometric identities, we know that;
cos 2θ = (cos² θ - sin²θ)
cos²θ + sin²θ = 1
sin 2θ = 2sinθcosθ
Thus;
(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:
>> cos 2θ/(1 + sin 2θ)
This is equal to the left hand side.
Thus, it is verified.
