Question

If sinA =1/3, then find the value of cosAcosecA+tanAsecA

Answer 1

$\textbf{Answer}$

We will use following trigonometric identities in the answer,
$\textbf{sin^2 x + cos^2 x = 1}$
$\textbf{tanx = sinx/cosx}$
$\textbf{cosx = 1 / secx}$

We are given that,
sinA = 1/3

We know that,

sin^2 A + cos^2 A = 1

=> cos^2 A = 1 - sin^2 A

=> cos^2 A = 1 - (1/9)

=>cos^2 A = 8/9 ---------(1)

=>cos A = 2√2 / 3 -------(2)

We need to find the value of,

cosAcosecA + tanAsecA

= (cosA / sinA) + (sinA)/(cosA.cosA)

= (2√2)/(3/3) + {1 / (3×8/9)} [By using (1) & (2)]

= 2√2 + (3/8)

= (16√2 + 3) / 8

So

cosAcosecA+tanAsecA = (16√2 + 3)/8

$\textbf{Hope It Helps}$

$\textbf{Thanks}$