Answer:

This means that A is in Quadrant I and B is in Quadrant I

Question 2:

Answer:

This means that A is in Quadrant II and B is in Quadrant I

Answer:

,

This means that A is in Quadrant III and B is in Quadrant IV

Answer:

This means that A is in Quadrant III and B is in Quadrant I

Answer:

This means that A is in Quadrant II and B is in Quadrant IV

,

Find the following:

Answer:

This means that A is in Quadrant II and B is in Quadrant I

Question 7: Evaluate the following:

Answer:

Question 8: , where A lies in the second quadrant and B in the third quadrant, find the values of the following:

Answer:

where A lies in the second quadrant and B in the third quadrant

Answer:

RHS. Hence proved.

Answer:

RHS. Hence proved.

Question 11:

Answer:

Question 12:

Answer:

Note:

RHS. Hence proved.

Note:

RHS. Hence proved.

Note:

RHS. Hence proved.

Answer:

Question 14:

Answer:

Question 15: Prove that

Answer:

Substituting it back

Since:

Question 16: Prove that:

Answer:

Question 17: Prove that:

Answer:

Answer:

RHS

LHS. Hence proved.

Answer:

Using Componendo and Dividendo

Answer:

Hence proved.

, find the value of

Answer:

Similarly,

, prove that

Answer:

Hence proved.

, prove that:

Answer:

Answer:

Answer:

Given

. Hence proved.

Answer:

Given:

… … … i)

… … … ii)

Solving i) and ii) we get

Also

are two different values of lying between which satisfy the equation , find the value of

Answer:

Given

Eliminating

Squaring both sides

are roots of equation

Similarly

Eliminating

Squaring both sides

are roots of equation

, show that

Answer:

Given,

Question 29: Prove that:

Answer:

RHS. Hence proved.

RHS. Hence proved.

RHS. Hence proved.

, prove that

Answer:

Hence Proved.

, show that

Answer:

. Hence proved.

Question 32: If angle is divided into two parts such that the tangents of one parts is times the tangent of other, and is their difference, then show that

Answer:

Let be the two parts

Applying componendo and dividendo

Answer:

Dividing both numerator and denominator by

Hence proved.

Question 34: are two solutions of the equation , then find the values of

Answer:

Squaring both sides

are the roots then

Squaring both sides

are the roots then

Now