(i) If cos A = ; find the value of : (ii) If (2cos 2A - 1) (tan3A - 1) = 0; find all possible values of angle A.

(i) Given: cos A = ⇒ Let base be 9a and hypotenuse be 41a. Using Pythagoras theorem, Hypotenuse2 = Base2 + Perpendicular2 ⇒ (41a)2 = (9a)2 + Perpendicular2 ⇒ 1681a2 = 81a2 + Perpendicular2 ⇒ Perpendicular2 = 1681a2 - 81a2 ⇒ Perpendicular2 = 1600a2 ⇒ Perpendicular = ⇒ Perpendicular = 40a sin A = = = ⇒ (sin A)2 = ⇒ sin2 A = And, cot A = = = ⇒ (cot A)2 = ⇒ cot2 A = Now, the value of Hence, the value of . (ii) Given: (2cos 2A - 1) (tan3A - 1) = 0 ⇒ (2cos 2A - 1) = 0 or (tan3A - 1) = 0 ⇒ 2cos 2A = 1 or tan3A = 1 ⇒ cos 2A = or tan3A = tan 45° ⇒ cos 2A = cos 60° or tan3A = tan 45° ⇒ 2A = 60° or 3A = 45° ⇒ A = ⇒ A = 30° or A = 15° Hence, the value of A = 30° or 15°.

If 4 cos² A - 3 = 0 and 0° ≤ A ≤ 90°; find:
(i) angle A
(ii) cos 3 A
(iii) tan² A + cos² A

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Find the value of angle A, if :
(i) sin 2A = 1
(ii) 2 sin 2A = 1
(iii) 2 sin A = 1

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Mathematics

(i) If cos A = ; find the value of : (ii) If (2cos 2A - 1) (tan3A - 1) = 0; find all possible values of angle A.

Trigonometrical Ratios

Related Questions

If 4 cos² A - 3 = 0 and 0° ≤ A ≤ 90°; find:
(i) angle A
(ii) cos 3 A
(iii) tan² A + cos² A

Find the value of angle A, if :
(i) sin 2A = 1
(ii) 2 sin 2A = 1
(iii) 2 sin A = 1

Mathematics

(i) If cos A = ; find the value of : (ii) If (2cos 2A - 1) (tan3A - 1) = 0; find all possible values of angle A.

Trigonometrical Ratios

Related Questions

If 4 cos2 A - 3 = 0 and 0° ≤ A ≤ 90°; find:(i) angle A(ii) cos 3 A(iii) tan2 A + cos2 A

Find the value of angle A, if :(i) sin 2A = 1(ii) 2 sin 2A = 1(iii) 2 sin A = 1

If 4 cos² A - 3 = 0 and 0° ≤ A ≤ 90°; find:
(i) angle A
(ii) cos 3 A
(iii) tan² A + cos² A

Find the value of angle A, if :
(i) sin 2A = 1
(ii) 2 sin 2A = 1
(iii) 2 sin A = 1