Question

Anybody brainilist?
Cos50/1+sin50 ?
1)cot20 2)tan20 3)tan25 4)tan 70

Answer 1

the answer is 2)tan20.

Answer 2

$\frac{cos\ 50}{1 + sin\ 50 } =tan\ 20$

Solution:

Given that:

$\frac{cos\ 50}{1 + sin\ 50 }$

We know,

$cos\ (90 - \theta ) = sin\ \theta$

$sin(90 - \theta) = cos\ \theta$

Therefore,

$\frac{cos\ 50}{1 + sin\ 50 } \\\\\frac{sin\ (90 - 50) }{ 1 + cos(90-50) } \\\\\frac{sin\ 40 }{ 1 + cos\ 40 }$

We know,

$sin\ 2\ \theta = 2sin\ \theta\ cos\ \theta \\\\1 + cos\2 \theta = 2cos^2 \theta$

Therefore,

$\frac{sin\ 40 }{ 1 + cos\ 40 } = \frac{2sin\ 20\ cos\ 20}{2cos^2\ 20}\\\\\frac{sin\ 40 }{ 1 + cos\ 40 } = \frac{sin\ 20}{cos\ 20 } \\\\\frac{sin\ 40 }{ 1 + cos\ 40 } = tan\ 20$

Thus,

$\frac{cos\ 50}{1 + sin\ 50 } =tan\ 20$

Learn more:

Find the value of 4sin50° - √3tan50°

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Find the value of sin 50 degree/ cos 40 degree + cosec 40 degree/ sec 50 degree -4 cos 50 degree cosec 40 degree

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