Introduction to Trigonometry Exercise 8.4

NCERT solutions for Maths Introduction to Trigonometry 

NCERT Solutions for Class 10 Maths Introduction to Trigonometry

1. Express the trigonometric ratios and in terms of

Ans. For

By using identity

For

By using identity

=

For

2. Write the other trigonometric ratios of A in terms of

Ans. For

By using identity,

=

For

For

By using identity

For

=

For

NCERT Solutions for Class 10 Maths Exercise 8.4

3. Evaluate:

(i)

(ii)

Ans. (i)

=

=

=

(ii)

=

=

= = 1

NCERT Solutions for Class 10 Maths Exercise 8.4

4. Choose the correct option. Justify your choice:

(i) =

(A) 1

(B) 9

(C) 8

(D) 0

(ii) =

(A) 0

(B) 1

(C) 2

(D) none of these

(iii) =

(A)

(B)

(C)

(D)

(iv) =

(A)

(B)

(C)

(D) none of these

Ans. (i) (B)

=

=

(ii)(C)

=

=

=

=

=

= = 2

(iii)(D)

=

=

= =

=

(iv)(D) =

= =

= =

NCERT Solutions for Class 10 Maths Exercise 8.4

5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

(i)

(ii)

(iii)

(iv)

(v) , using the identity

(vi)

(vii)

(viii)

(ix)

(x)

Ans. (i) L.H.S.

=

=

=

=

=

=

=

= = R.H.S.

(ii) L.H.S.

=

=

=

= =

= = = R.H.S

(iii) L.H.S.

=

=

=

=

=

=

=

= =

=

(iv) L.H.S.

= =

=

=

= = R.H.S.

(v) L.H.S.

Dividing all terms by

= =

=

=

=

= = R.H.S.

(vi) L.H.S.

=

=

=

= =

= = R.H.S.

(vii) L.H.S.

=

=

=

= =

= = R.H.S

(viii) L.H.S.

=

=

=

=

=

=

=

= R.H.S.

(ix) L.H.S.

=

=

= =

=

Dividing all the terms by ,

=

=

= = R.H.S.

(x) L.H.S. =

= = = R.H.S.

Now, Middle side = =

=

= =

= = R.H.S.