Solve for x ∈ W, 0° x 90°. (i) 3 tan 2 2x = 1 (ii) tan 2 x = 3(sec x - 1)

(i) Given, ⇒ 3 tan 2 2x = 1 ⇒ tan 2 2x = ⇒ tan 2x = ⇒ tan 2x = ⇒ tan 2x = tan 30° ⇒ 2x = 30° ⇒ x = = 15°. Hence, x = 15°. (ii) Given, ⇒ tan 2 x = 3(sec x - 1) ⇒ sec 2 x - 1 = 3sec x - 3 ⇒ sec 2 x - 3 sec x - 1 + 3 = 0 ⇒ sec 2 x - 3 sec x + 2 = 0 ⇒ sec 2 x - 2 sec x - sec x + 2 = 0 ⇒ sec x(sec x - 2) - 1(sec x - 2) = 0 ⇒ (sec x - 1)(sec x - 2) = 0 ⇒ sec x - 1 = 0 or sec x - 2 = 0 ⇒ sec x = 1 or sec x = 2 ⇒ sec x = sec 0° or sec x = sec 60° ⇒ x = 0° or x = 60° Hence, x = 0° or 60°.

The mean of the following frequency distribution is 50, but the frequencies f₁ and f₂ in class 20-40 and 60-80 respectively are not known. Find these frequencies.
Class Frequencies
0-20 17
20-40 f₁
40-60 32
60-80 f₂
80-100 19
Given that the sum of frequencies is 120.

Class	Frequencies
0-20	17
20-40	f₁
40-60	32
60-80	f₂
80-100	19

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Mathematics

Solve for x ∈ W, 0° ≤ x ≤ 90°.
(i) 3 tan² 2x = 1
(ii) tan² x = 3(sec x - 1)

Trigonometric Identities

Related Questions

The mean of the following frequency distribution is 50, but the frequencies f₁ and f₂ in class 20-40 and 60-80 respectively are not known. Find these frequencies.
Class Frequencies
0-20 17
20-40 f₁
40-60 32
60-80 f₂
80-100 19
Given that the sum of frequencies is 120.

Mathematics

Solve for x ∈ W, 0° ≤ x ≤ 90°.(i) 3 tan2 2x = 1(ii) tan2 x = 3(sec x - 1)

Trigonometric Identities

Related Questions

The mean of the following frequency distribution is 50, but the frequencies f1 and f2 in class 20-40 and 60-80 respectively are not known. Find these frequencies.ClassFrequencies0-201720-40f140-603260-80f280-10019Given that the sum of frequencies is 120.

Solve for x ∈ W, 0° ≤ x ≤ 90°.
(i) 3 tan² 2x = 1
(ii) tan² x = 3(sec x - 1)

The mean of the following frequency distribution is 50, but the frequencies f₁ and f₂ in class 20-40 and 60-80 respectively are not known. Find these frequencies.
Class Frequencies
0-20 17
20-40 f₁
40-60 32
60-80 f₂
80-100 19
Given that the sum of frequencies is 120.