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aleksandr82 [10.1K]
2 years ago
10

(1+sinx/cosx)+(cosx/1+sin)

Mathematics
1 answer:
Licemer1 [7]2 years ago
5 0

( 1 + sinx / cosx ) + ( cosx / 1 + sinx ) =

_________________________________

(1 + sinx)(1 + sinx)/cosx(1 + sinx)

+

(cosx)(cosx)/(1 + sinx)(cosx) =

_________________________________

(1 + sinx)^2 /cosx(1 + sinx)

+

(cosx)^2/cosx(1 + sinx) =

_________________________________

1 + 2sinx + sin^2 x/cosx(1 + sinx)

+

cos^2 x/cosx(1 + sinx) =

_________________________________

1 + sin^2 x + cos^2 x + 2sinx / cosx(1 + sinx) =

<h2>Hint : </h2><h2>Sin^2 x + Cos^2 x = 1</h2>

1 + 1 + 2sinx / cosx(1 + sinx) =

2 + 2sinx / cosx(1 + sinx) =

2(1 + sinx)/cosx(1 + sinx) =

( 1 + sinx) simplifies from the face and the denominator of the fraction

2/cosx

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The size of the angle QUP in the system formed by the <em>equilateral</em> triangle QUR, the <em>equilateral</em> triangle PUT and the square RUTS is equal to 150°.

<h3>How to determine a missing angle within a geometrical system</h3>

By Euclidean geometry we know that squares are quadrilaterals with four sides of <em>equal</em> length and four <em>right</em> angles and triangles are <em>equilateral</em> when its three sides have <em>equal</em> length and three angles with a measure of 60°. In addition, a complete revolution has a measure of 360°.

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<em>m∠QUR + m∠QUP + m∠PUT + m∠RUT =</em> 360

60 <em>+ m∠QUP +</em> 60 <em>+</em> 90 <em>= 360</em>

<em>m∠QUP +</em> 210 <em>=</em> 360

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The size of the angle QUP in the system formed by the <em>equilateral</em> triangle QUR, the <em>equilateral</em> triangle PUT and the square RUTS is equal to 150°. \blacksquare

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/13805601

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