Question

3. Answer any ten question

a) Prove that A (BAC) = (ANBA(
AC).
b) Prove that A - - (BUC) = (A - B - C.
c) Prove that
A UBUCI = A + B + C + ABAC - AN BI - BACILICA
d) in a group of people; 37 like Coffee, 52 like tea and each person in the group likes
at least one of the two drinks. 19 people like both tea and Coffee, how many
people are in the group?
e) Let f(x) = V1 + x, g(x) = V1 - x then find f + g and f-g.
sin(180° +A) tan(360°-A) sec (180°- A)
f) Show that
= tans A.
cos? (900+A)cosec- A sin(1800-A)
Prove that sin 50 = 16sinso
16sins - 20sino + 5 sin 8.
h)
Prove that cos A =
1- tan24
it tanza
2
i) Prove that cot A - CSC 2A = cot 2A.
j) Prove that sec 0 + tan 8 = tan(+)
cot A-3 cot A
k) Prove that cot 3A
3 Col²A-1
1) Prove that sin 20° sin 40° sin 60° sin 80º =
3
16​

Answer 1

Answer:

Let C denote the set of people who like coffee, and T denote the set of people who like tea

n(C∪T)=70,n(C)=37,n(T)=52

We know that:

n(C∪T)=n(C)+n(T)−n(C∩T)

∴70=37+52−n(C∩T)

⇒70=89−n(C∩T)

⇒n(C∩T)=89−70=19