Without using trigonometric tables, find the values of; (i) (3sin2 45 + 2cos260 ) (ii) (3cos2 30 + tan260 ) (iii) (cos 0 + sin 45 + sin 30 )(sin 90 - cos 45 + cos 60 ) (iv) 2 cos 45 cos 60 + 2 sin 30 tan 60 - cos 0 (v) tan230 + sin260 - 3 cos260 + tan260 - 2 tan245 (vi)

Question

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(i) As, sin2 45 = (sin 45 )2 = and cos2 60 = (cos 60 )2 = Substituting values we get : (3sin2 45 + 2cos260 ) = = = = 2. Hence, 3 sin2 45 + 2 cos260 = 2. (ii) As, cos2 30 = (cos 30 )2 = and tan2 60 = (tan 60 )2 = = 3 Therefore, 3cos2 30 + tan260 = + 3 = + 3 = . Hence, 3cos2 30 + tan260 = . (iii) (cos 0 + sin 45 + sin 30 )(sin 90 - cos 45 + cos 60 ) Hence, (cos 0 + sin 45 + sin 30 )(sin 90 - cos 45 + cos 60 ) = . (iv) cos 45 cos 60 + 2 sin 30 tan 60 - cos 0 = 2 = 1 + 3 - 1 = 3. Hence, 2 cos 45 cos 60 + 2 sin 30 tan 60 - cos 0 = 3. (v) As, cos2 60 = (cos 60 )2 = and tan2 30 = (tan 30 )2 = tan2 45 = (tan 45 )2 = 1 tan2 60 = (tan 60 )2 = ()2 = 3 sin2 60 = (sin 60 )2 = Therefore, tan230 + sin260 - 3 cos260 + tan260 - 2 tan245 Hence, tan230 + sin260 - 3 cos260 + tan260 - 2 tan245 = . (vi) As, cos2 45 = (cos 45 )2 = sin2 45 = (sin 45 )2 = tan2 60 = (tan 60 )2 = ()2 = 3 Therefore, = = Hence, .

Mathematics

Without using trigonometric tables, find the values of; (i) (3sin2 45 + 2cos260 ) (ii) (3cos2 30 + tan260 ) (iii) (cos 0 + sin 45 + sin 30 )(sin 90 - cos 45 + cos 60 ) (iv) 2 cos 45 cos 60 + 2 sin 30 tan 60 - cos 0 (v) tan230 + sin260 - 3 cos260 + tan260 - 2 tan245 (vi)

Trigonometrical Ratios

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Without using trigonometric table, find the values of:
(i) sin 60° cos 30° + cos 60° sin 30°
(ii) sin 45° cos 30° - cos 45° sin 30°
(iii) cos 60° cos 45° + sin 60° sin 45°
(iv) cos 90° + cos² 45° sin 30° tan 45°

Mathematics

Without using trigonometric tables, find the values of; (i) (3sin2 45 + 2cos260 ) (ii) (3cos2 30 + tan260 ) (iii) (cos 0 + sin 45 + sin 30 )(sin 90 - cos 45 + cos 60 ) (iv) 2 cos 45 cos 60 + 2 sin 30 tan 60 - cos 0 (v) tan230 + sin260 - 3 cos260 + tan260 - 2 tan245 (vi)

Trigonometrical Ratios

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Without using trigonometric table, find the values of:(i) sin 60° cos 30° + cos 60° sin 30°(ii) sin 45° cos 30° - cos 45° sin 30°(iii) cos 60° cos 45° + sin 60° sin 45°(iv) cos 90° + cos2 45° sin 30° tan 45°

Without using trigonometric table, find the values of:
(i) sin 60° cos 30° + cos 60° sin 30°
(ii) sin 45° cos 30° - cos 45° sin 30°
(iii) cos 60° cos 45° + sin 60° sin 45°
(iv) cos 90° + cos² 45° sin 30° tan 45°