Q13 of 27 Page 301

If A = 30°, verify that:

(i)


(ii)


(iii)

(i) To prove:- sin 2A =


A = 30°


∴ To show:- sin 60° =


Consider L.H.S. = =


=


= =


= √3/2


= sin 60° = R.H.S.


∴ R.H.S. = L.H.S.


Hence, verified.


(ii) To show:- cos 2A =


A = 30°


∴ To show:- cos 60° =


Consider R.H.S. = =


= 2/4 = 1/2 = cos 60° = L.H.S.


∴ R.H.S. = L.H.S.


Hence, verified.


(iii) To show:- tan2A =


A = 30°


∴ To show:- tan 60° =


Consider R.H.S. = = =


= 3/√3 = √3


= tan 60° = L.H.S.


∴ R.H.S. = L.H.S.


Hence, verified.


More from this chapter

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11

Verify each of the following:

(i) sin 60° cos 30° — cos 60° sin 30° = sin 30°


(ii) cos 60° cos 30° + sin 60° sin 30° = cos 30°


(iii) 2 sin 30° cos 30° = sin 60°


(iv) 2 sin 45° cos 45° = sin 90°

 12

If A = 45°, verify that:

(i) sin 2A = 2 sin A cos A


(ii) cos 2A = 2 cos2A —1 = 1— 2 sin2A

 14

If A = 60° and B = 30°, verify that:

(i) sin (A + B) = sin A cos B + cos A sin B


(ii) cos (A + B) = cos A cos B — sin A sin B

 15

If A = 60° and B = 30°, verify that:

(i) sin (A — B) = sin A cos B — cos A sin B


(ii) cos (A — B) = cos A cos B + sin A sin B


(iii)