Trigonometry Answers

How do you simplify this problem?
B=90°-83°36′
≈__°__′

IN a hospital, there are 200 beds for patients. OF these, 120 are occupied by males and remaining by females. 20% of the males and 40% of the females are suffering from malaria and rest of them for dengue. If a patient is selected at random, find the probability that he/she is a :A female patientB - MAle patientC - male patient suffering from malariaD - Female patient suffering from dengue

cot ( 90-a) - tan (180-b) ÷ tan (90-a) + cot b

1080•cos98

Find theta for 0 degrees equal or less then theta less then 360 degrees that satisfies the stated condition.

tan theta = -0.6 and sin theta is less then zero

HELLO MADAM, my doubt is, a rhombus has one of its sides as 10cm and one angle as 40 degree. Find the area of the rhombus

if the ration of three sides of a triangle is a:b:c=7:8:9 then show that CosA:CosB:CosC=14:11:16.

2sin45 + 2cos45

If TanA=ptanB then prove that Sin(A+B)=(p+1)(sin(A-B))/(p-1)

I need help with the following proofs.
a.) cos(nθ)=cos((n-2)θ)-2sinθsin((n-1)θ)
b.) (sin(x/2)+sin(x))/(cos(x/2)-cos(x))=cot(x/4)
c.) (sin∝-cos∝+1)/(sin∝+cos∝-1)=(sin∝+1)/cos∝
d.) tan(x/2)=(1-cos(x)+sin(x))/(1+cos(x)+sin(x))