Question

if cosecA+cotA=5 then evaluate secA

Answer 1

Answer:

cosecA=1/sinA

cotA=cosA/sinA

Therefore, cosecA+cotA=(1+cosA)/sinA…..Eq 1

Now, 1+cosA=2×cos(A/2)×cos(A/2)... Eq 2… Numerator

And sinA=2sin(A/2)cos(A/2)…. Eq 3…. Denominator

Substituting Eq 2 and Eq 3 in Eq 1, we get:

Numerator/denominator= 11/2 as RHS is given in question

cot (A/2)=11/2

Or tan(A/2)=2/11

We know that

tanA=[(2 tan(A/2)]/[1-sqr(tan(A/2)

Where sqr is a squaring function(ex: sqr(2)=4)

Substituting value of tan(A/2) in the above eq, we get

tanA=44/117.

It seems difficult approach, but I feel it is the shortest path if you know trigonometric identites. Its very important to learn all the trigonometric identities.

Step-by-step explanation:

use this formula