Question

What is the value of (tan 5A)(tanA)? ​

Answer 1

Answer:

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Let A= 18°

Therefore, 5A=90°

= 2A+3A =90°

=20=90° - 3A

Taking sine on both sides,we get

sin 2A = sin(90°-3A )=cos 3A

3

= 2 sin A cos A - 4 cos 3 A - 3 cos A

3

= 2sin A cos A-4 cos A-4 cos3 A + 3cos A = 0

2

= cos A ( 2 sin A -4 cos2 A+3) =0

Dividing both sides by cos A = cos 18° =/= 0, we get

2

= 2 sin 0-4 ( 1- sin2 A) +3 =0

2

= 4 sin2 A +2 sin A -1 =0, which is a quadratic in sin A

-4(4)(-1)

-2+2 5 ^

4

= sin 0 = -1 +54

Therefore, sin 18° =sin A = -1+54

Therefore, tan 54°=

5+1

10-2

/

/5+110-25

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Answer 2

Answer:

Step-by-step explanation:

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