Question

If cosec(theta)=25/24 then find sin^2(theta)+cos^2(theta)

Answer 1

always sin^2(theta)+cos^2(theta)= 1
look
given that cosec(theta)=25/24
so sin(theta)=24/25
so sin^2(theta)=576/625
by this we can get cos^2(Theta)=47/625
therefore sin^2(theta)+cos^2(theta)=576/625+47/626=625/625=1

Answer 2

cosec∅ = 25/24

we know that cosec∅ = hypotenuse / opposite side to ∅.

Hypotenuse ²- opposite side²=adjacent side²

25²-24²=adjacent side

adjacent side =√49=7

Now,sin∅=24/25

cos∅=7/25

sin²∅+cos²∅

=(24/25)²+(7/25)²

=576+49/625

=625/625

=1

sin²∅+cos²∅=1