Get the answer to "What is the value of 1cos⁡18∘sin⁡9∘+1cos⁡18∘cos⁡9∘?"

Inyalan0

Answered question

2021-12-26

What is the value of

\frac{1}{{\cos 18}^{\circ} {\sin 9}^{\circ}} + \frac{1}{{\cos 18}^{\circ} {\cos 9}^{\circ}}

usaho4w

Beginner2021-12-27Added 39 answers

Hint:
Multiply the num/denom of the first fraction by

2 \cos (9^{\circ})

and the num/denom of the second fraction by

2 \sin (9^{\circ})

and use

2 \sin (x) \cos (x)

you will get

\frac{4 ({\cos 9}^{\circ} + {\sin 9}^{\circ})}{{\sin 36}^{\circ}}

Finish by using the sum formulas for

\sin and \cos

{\cos 9}^{\circ} + {\sin 9}^{\circ} = {\sin 81}^{\circ} + {\sin 9}^{\circ} = 2 {\sin 45}^{\circ} {\cos 36}^{\circ}

Mary Herrera

Beginner2021-12-28Added 37 answers

hint

a \cos x + b \sin x =

\sqrt{a^{2} + b^{2}} \cos (θ - x)

if a=b=1 then

θ = 45^{\circ}

and

{\cos 9}^{\circ} + {\sin 9}^{\circ} = \sqrt{2} \cos (45 - 9)

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