Use double- and half-angle formulas to find the exact value of the expression: P

ringearV

ringearV

Answered question

2021-08-16

Use double- and half-angle formulas to find the exact value of the expression: tanπ12

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-08-17Added 99 answers

Use the trigonometry identity:
tan2α=2tanα1tan2α
Trigonometry table:
tan2α=tan(π6)=13
call tan(π12)=t, we get:
13=2t1t2
cross multiply
t2+23t1=0
Solve this quadratic equation for t
D=d24ac=4(3)+4=16d=±4
Therefore two real roots:
t=tan(π12)=b2a±d2a=232±42=3±2
Since tan(π12) is positive, therefore
tan(π12)=23
Check by calculator
tan(π12)=tan15=0.27
23=21.73=0.27
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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