Find the minimum value of sin <mrow class="MJX-TeXAtom-ORD"> 2 </mrow>

Jeramiah Campos

Jeramiah Campos

Answered question

2022-06-16

Find the minimum value of sin 2 θ + cos 2 θ + sec 2 θ + csc 2 θ + tan 2 θ + cot 2 θ

Answer & Explanation

Layla Love

Layla Love

Beginner2022-06-17Added 29 answers

Hint:
We can use the Pythagorean identities sin 2 θ + cos 2 θ = 1 , sec 2 θ = tan 2 θ + 1 and csc 2 θ = cot 2 θ + 1 , giving us
sin 2 θ + cos 2 θ + sec 2 θ + csc 2 θ + tan 2 θ + cot 2 θ = 3 + 2 tan 2 θ + 2 cot 2 θ = 3 + 2 ( tan 2 θ + 1 tan 2 θ )
Ayanna Trujillo

Ayanna Trujillo

Beginner2022-06-18Added 13 answers

Hint:
sin 2 θ + cos 2 θ + sec 2 θ + csc 2 θ + tan 2 θ + cot 2 θ
= sec 2 θ + csc 2 θ + sec 2 θ + csc 2 θ 1 = 2 s e c 2 θ + 2 csc 2 θ 1

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