Question

Find the magnitude of angle A, if: 2 tan 3A . cos 3A - tan 3A + 1 = 2 cos 3A

( Trigonometrical ratios of standard angles )

Answer 1

Step-by-step explanation:

Given Equation is 2 tan3A. cos3A - tan 3A + 1 = 2 cos 3A

⇒ 2 tan3A cos 3A - tan 3A + 1 - 2 cos 3A = 0

⇒ tan 3A(2 cos3A - 1) - (2cos3A - 1) = 0

⇒ (tan 3A - 1)(2cos 3A - 1) = 0

⇒ tan 3A = 1 (or) 2 cos 3A - 1 = 0

(i) When tan 3A = 1:

⇒ tan 3A = 1

⇒ tan 3A = tan 45

⇒ 3A = 45

⇒ A = 15°

(ii) When 2cos3A = 1:

⇒ 2 cos 3A = 1

⇒ cos 3A = 1/2

⇒ cos 3A = cos 60

⇒ 3A = 60

⇒ A = 20°

Therefore, Magnitude of A is 15° (or) 20°

Hope it helps!

Answer 2

Answer:

$2 \tan3a \cos3a - \tan3a + 1 = 2 \cos3a$

$2 \tan3a \cos3a - \tan3a - 2 \cos3a + 1 = 0$

$\tan3a(2 \cos3a - 1) - 1(2 \cos3a - 1) = 0$

$\tan3a( 2\cos3a - 1)(2 \cos3a - 1) = 0$

Either tan3A -1 =0 or 2cos3A -1=0

$\tan3a = 1 \: or \: \cos3a = \frac{1}{2}$

$\tan3a = \tan45 \: or \: \cos3a = \cos60$

3A=45 or 3A=60

A=15 or A=20°

Thus A=15° or 20°