Question 1: Express each of the following as a sum or difference of sine and cosines:

i) ii) iii) iv)

Answer:

i)

ii)

iii)

iv)

Question 2: Prove that:

i) ii) iii)

Answer:

i)

RHS. Hence proved.

ii)

RHS. Hence proved.

iii)

RHS. Hence proved.

Question 3: Show that:

i) ii)

Answer:

i) LHS

RHS. Hence Proved.

ii) LHS

RHS. Hence Proved.

Question 4: Prove that

Answer:

LHS

RHS

Question 5: Prove that:

i) ii)

iii) iv)

v) vi)

vii) viii)

Answer:

i) LHS

RHS. Hence proved.

ii) LHS

RHS. Hence proved.

iii) LHS

RHS. Hence proved.

iv) LHS

RHS. Hence Proved.

v) LHS

RHS. Hence proved.

vi) LHS

RHS. Hence proved.

vii) LHS

RHS. Hence proved.

viii) LHS

RHS. Hence proved.

Question 6: Show that:

i)

ii)

Answer:

i) LHS

RHS. Hence proved.

ii) LHS

RHS. Hence proved.

Question 7: Prove that:

Answer:

LHS

RHS. Hence proved.

Question 8: If , show that the maximum value of is

Answer:

Let

Now we know

Therefore the max value of is