Question

If triangle ABC And right angle at c then the value of cosec(A +B)

Answer 1

Answer:

The value of cosec(A+B) is 1

Step-by-step explanation:

$\textsf{Given:}$

$\textsf{ABC is right angled at C}$

$\textsf{since sum of the angles is }180^{\circ},$

$\mathsf{A+B+C=180^{\circ}}$

$\mathsf{\implies\,A+B=180^{\circ}-90^{\circ}}$

$\mathsf{\implies\,A+B=90^{\circ}}$

$\textsf{Now}$

$\mathsf{cosec(A+B)}$

$\mathsf{=cosec\,90^{\circ}}$

$\mathsf{=\frac{1}{sin\,90^{\circ}}}$

$\mathsf{=\frac{1}{1}}$

$\mathsf{=1}$

$\mathsf{\implies\,cosec(A+B)=1}$

Answer 2

The value of cosec(A+B) = 1

Step-by-step explanation:

In a triangle ABC , right angle at C

i.e $\angle C = 90$°

then,

A+B+C = 180°  (angle sum property)'

putting the value of C

A+B+ 90°= 180°

A+B= 180°-90°

A+B= 90°

we have to find the value of cosec(A+B)

putting the value of A+B

cosec (90°)

value of cosec 90°= 1

hence,

the value of cosec(A+B) = 1

#Learn more:

Triangle ABC is a right triangle, right at c then the value of cosec spuare A - tan square B is​

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