Question

if A+B=90° and sec A=5/3 ,then find the value of cosec B.

Answer 1

cosa=3/5
sina=4/5
since a+b=90
b=90-a
and sin(90-a)=sina=sinb=4/5
cosec b=5/4

Answer 2

Answer:

Using trigonometric identity:

• $\sec x = \frac{1}{\cos x}$

• $\cos (90-x) = \sin x$
• $\csc x = \frac{1}{\sin x}$

As per the statement:

if A+B=90° and sec A=5/3

sec A = 5/3

Apply the trigonometry identity:

$\frac{1}{\cos A} =\frac{5}{3}$

By cross multiply we have;

$3 = 5\cos A$

⇒$\cos A = \frac{3}{5}$         ....[1]

It is also given:

$A+B = 90^{\circ}$

then;

$A = 90^{\circ}-B$

Substitute in [1] we have;

$\cos (90^{\circ}-B) = \frac{3}{5}$

Apply the trigonometry identity:

$\sin B = \frac{3}{5}$

then;

$\frac{1}{\csc B} = \frac{3}{5}$

⇒$\csc B = \frac{5}{3}$

therefore, the value of cosec B is 5/3