Question 1: In a right angles triangle , right angled at , if , find all the six trigonometric ratios of .

Answer:

Given

Therefore,

;

;

;

Question 2: If , find the value of the other five trigonometric ratios.

Answer:

Given

By Pythagoras theorem, we have

;

;

;

Question 3: If , find the value of

Answer:

Given , therefore by Pythagoras theorem,

; ;

Hence

Question 4: If , show that

Answer:

Given

By Pythagoras theorem, we have

and

Hence,

Question 5: In , right angles at , if and , show that

Answer:

Given

By Pythagoras theorem, we have

and

and

LHS = RHS.

Hence proved.

Question 6: If , prove that

Answer:

Given

By Pythagoras theorem, we have

; ;

LHS

RHS

Therefore LHS = RHS. Hence proved.

Question 7: In the given figure, and . Determine (i) ii) iii) iv)

Answer:

By Pythagoras theorem, we have

Therefore:

i)

ii)

iii)

iv)

Question 8: In a , right angles at and , i) is ii) is

Answer:

Given

i)

ii)

Question 9: If , show that

Answer:

LHS

RHS. Hence proved.

Question 10: If , find the value of

Answer:

Squaring on both sides,

Question 11: If , evaluate i) ii)

Answer:

i)

ii)

Question 12: If , check if

Answer:

Given

LHS

RHS

Therefore LHS = RHS. Hence proved.

Question 13: If , find the value of

Answer:

Given

Dividing both the numerator and denominator by we get

Question 14: If , find

Answer:

By Pythagoras theorem,

Therefore, and

Hence

Question 15: If , find the value of

Answer:

By Pythagoras theorem,

Therefore ; ; ;

Question 16: If ; evaluate

Answer:

By Pythagoras theorem we get

Therefore ; ;

Therefore

Question 17: If , verify

Answer:

By Pythagoras theorem we get

Therefore ; ;

LHS

RHS =

Therefore LHS = RHS. Hence proved.

Question 18: If , prove that

Answer:

Given

By Pythagoras theorem,

Therefore ; ; ; ;

LHS =

Question 19: If , find

Answer:

Given

By Pythagoras theorem, we get

Therefore and

Hence

Question 20: If , find

Answer:

Given , find

Question 21: If and are acute angles such that , then show that

Answer:

Since

(angles opposite equal sides of a triangle are equal)

Question 22: In a triangle, and are acute angles such that , show that

Answer:

and

Given that

(angles opposite equal sides of a triangle are equal)

Question 23: If is an acute angle such that , find the value of

Answer:

Given

Therefore

By Pythagoras theorem, and

Hence,

Question 24: In adjoining figure, is right angles at and is the midpoint of . , and . Find i) ii) iii)

Answer:

By Pythagoras theorem

Therefore i)

ii) By Pythagoras theorem

Therefore and

iii)