Question

if tan theta is 5/12 and is not in fourth quadrant then tan( 90+theta ) -sin 180-theta /sin 270 -theta + cosec 360-theta ?
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Answer 1

Answer:

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Answer 2

Answer:

Answers of the given expressions are :

=2172/1565 , - 1572/1565

Given:

tan θ = 5/12

and  θ is not in fourth quadrant.

To Find:

Find the value of {tan (90+ θ) -sin(180 - θ)}/{sin (270 - θ) + cosec (360 - θ)}

Step-by-step explanation:

The above expression is :

{tan (90+ θ) -sin(180 - θ)}/{sin (270 - θ) + cosec (360 - θ)}

tan (90+ θ) = -cotθ

sin(180 - θ) = sin θ

sin (270 - θ) = -cos θ

cosec (360 - θ) = -cosec θ

So the above expression becomes :

{ - cotθ - sin θ}/ { -cos θ - cosec θ}

tan θ = 5 /12

perpendicular = 5

base  = 12

by triplet rule ,   hypotenuse = 13

As tan θ is positive than  θ is either in first quadrant or third quadrant.

If θ is in first quadrant:

cot θ = 12/5

sin θ = 5/13

cos θ = 12/13

cosec θ = 13/12

So the expression will be

{ - cotθ - sin θ}/ { -cos θ - cosec θ}

{-(12/5) -(5/13)}/{-(12/13) -(13/12)}

=2172/1565

If θ is in Third  quadrant:

cot θ = 12/5

sin θ =- 5/13

cos θ = -12/13

cosec θ = -13/12

So the expression will be

{ - cotθ - sin θ}/ { -cos θ - cosec θ}

{-12/5 +5/13}/{12/13 +13/12}

= - 1572/1565