The value of the expression (tan^4x+2 tan^2 x+1)cos^2 x, when x=pi/12 is equal to A)4(2−sqrt3); B)4(sqrt2+1); C) 16 cos^2 pi/12; D) 16 sin^2 pi/12

Tyrell Singleton

Tyrell Singleton

Answered question

2023-02-22

The value of the expression ( tan 4 x + 2 tan 2 x + 1 ) cos 2 x , when x = π 12 is equal to
A ) 4 ( 2 3 ) ; B ) 4 ( 2 + 1 ) ; C ) 16 cos 2 π 12 ; D ) 16 sin 2 π 12

Answer & Explanation

Makenna Martinez

Makenna Martinez

Beginner2023-02-23Added 7 answers

The appropriate choices are
A) 4 ( 2 3 )
D 16 sin 2 π 12
( tan 4 x + 2 tan 2 x + 1 ) cos 2 x = ( 1 + tan 2 x ) 2 sec 2 x = ( 1 + tan 2 x ) 2 1 + tan 2 x = 1 + t a n 2 x
Putting x = π 12
= 1 + t a n 2 π 12 = 1 + ( 2 3 ) 2 = 4 ( 2 3 )
Also,
16 cos 2 π 12 = 4 ( 3 + 1 2 ) 2 = 4 ( 2 + 3 ) 16 sin 2 π 12 = 4 ( 3 1 2 ) 2 = 4 ( 2 3 )

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