Question

Using trigonometric identities select the incorrect statement from the list below-
(i) cos8ѳ=cos24ѳ-sin24ѳ
(ii) sin8ѳ=2sin4ѳcos4ѳ
(iii) cos8ѳ= 1-sin24ѳ
(iv) cos8ѳ=2cos24ѳ-1

Answer 1

Given:

(i) cos8ѳ=cos24ѳ-sin24ѳ

(ii) sin8ѳ=2sin4ѳcos4ѳ

(iii) cos8ѳ= 1-sin24ѳ

(iv) cos8ѳ=2cos24ѳ-1

To find:

Using trigonometric identities select the incorrect statement from the list above.

Solution:

From given, we have,

(i) cos8ѳ=cos24ѳ-sin24ѳ

cos 2x = cos² x - sin² x

so, we have, cos 8∅ = cos² 4∅ - sin² 4∅

(ii) sin8ѳ=2sin4ѳcos4ѳ

sin 2x = 2 sin x cos x

so, we have, sin 8∅ = 2 sin 4∅ cos 4∅

(iii) cos8ѳ= 1-sin24ѳ

cos 2x = 1 - 2 sin² x

so, we have to get, cos 8∅ = 1 - 2 sin² 4∅

(iv) cos8ѳ=2cos24ѳ-1

cos 2x = 2 cos² x - 1

so, we get, cos 8∅ = 2 cos² 4∅ - 1

Therefore, option (iii) cos8ѳ= 1-sin24ѳ is incorrect, as cos2x = 1 - 2sin²x,  the constant "2" is missing