What is the value of \frac{1}{\cos 18^{\circ}\sin 9^{\circ}}+\frac{1}{\cos 18^{\circ}\cos 9^{\circ}}?

Inyalan0

Inyalan0

Answered question

2021-12-26

What is the value of 1cos18sin9+1cos18cos9?

Answer & Explanation

usaho4w

usaho4w

Beginner2021-12-27Added 39 answers

Hint:
Multiply the num/denom of the first fraction by 2cos(9) and the num/denom of the second fraction by 2sin(9) and use 2sin(x)cos(x)
you will get
4(cos9+sin9)sin36
Finish by using the sum formulas for sin and cos
cos9+sin9=sin81+sin9=2sin45cos36
Mary Herrera

Mary Herrera

Beginner2021-12-28Added 37 answers

hint
acosx+bsinx=
a2+b2cos(θx)
if a=b=1 then
θ=45
and
cos9+sin9=2cos(459)

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