Question

if 5cosA-12sinA=0 find the value of tanA+cosecA​

Answer 1

Answer:

y=17/(24–5)

y=17/19

Which is the required value.

Step-by-step explanation:

Let y=(sinA + cosA)/(2cosA-sinA)

Taking CosA as common from both numerator and denominator

y=[cosA((sinA/cosA)+(cosA/cosA))] /[cosA(2(cosA/cosA)-(sinA/cosA))]

Cancelling cosA and as we know sinA/cosA=tanA

So,

y=(tanA+1)/(2-tanA)

And we know

5cosA-12sinA=0

5cosA =12sinA

5=12[(sinA/cosA)]

TanA=5/12

Substitute the value of tanA in y

we get

y=(1+(5/12))/(2-(5/12))

y=[(12+5)/12]/[(12*2–5)/12]

Cancelling 12

y=17/(24–5)

y=17/19

Which is the required value.

Answer 2

Answer:

5cosA - 12 sinA = 0

5cosA = 12sinA

5/12 = tanA

cosecA = 1/sinA

cosecA = 13/5

tanA + cosecA = 5/12 + 13/5

=(25 + 65)/60

= 90/60

=3/2