Show trigonometric identity 1 &#x2212;<!-- − --> tan &#x2061;

shelohz0

shelohz0

Answered question

2022-05-21

Show trigonometric identity 1 tan θ 2 1 + tan θ 2 = sec θ tan θ

Answer & Explanation

ol5ick189

ol5ick189

Beginner2022-05-22Added 7 answers

Notice,
1 tan θ 2 1 + tan θ 2 = ( 1 tan θ 2 ) ( 1 + tan θ 2 ) ( 1 + tan θ 2 ) 2 = 1 tan 2 θ 2 1 + tan 2 θ 2 + 2 tan θ 2
= 1 1 + tan 2 θ 2 1 tan 2 θ 2 + 2 tan θ 2 1 tan 2 θ 2 = 1 sec θ + tan θ = sec θ tan θ sec 2 θ tan 2 θ = sec θ tan θ
Elisha Kelly

Elisha Kelly

Beginner2022-05-23Added 2 answers

1 tan x 2 1 + tan x 2 = cos x 2 sin x 2 cos x 2 + sin x 2 = 1 sin x cos x = sec x tan x .
(Change to sin and cos)-(Multiply N m and D m by N m )

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