Question

Find the value of
√3 cosec 20° - sec 20°




NO SPAM❗ ​

Answer 1

Question:

√3 cosec 20° - sec 20°

To Find:

Value

Solution:

$\sqrt{3 \: } cosec \: 20° - sec \: 20°$

As we know,

cosec 20⁰ = 1/sin20⁰ and sec 20⁰ = 1/cos20⁰

So,

$\sqrt{3 \: } cosec \: 20° - sec \: 20° \\ \frac{ \sqrt{3} }{sin \: 20°} - \frac{1}{cos \: 20°}$

2(√3/2/sin 20⁰ - 1/2/cos 20⁰)

$2 ( \frac{sin \: 60°}{sin \: 20° } - \frac{cos \: 60°}{cos \: 20°} ) \\2( \frac{sin60°cos20°−cos60°sin20°}{sin \: 20°cos \: 20°} ) \\2( \frac{sin(60°−20°)}{sin \: 20° \: cos20°}) \\2( \frac{sin40°}{sin20° \: cos \: 20°} ) \\ 2 \times \frac{2 \: sin20°cos20°}{sin20° \: cos 20°} \\ = 4$

Therefore 4 is the answer

Answer 2

Here is your correct answer mate

I hope this helps you