Question

If cosθ =4/5, then the value of cosecθ/(1+cosθ) is :-

(a) 7/5 (b) 2/7 (c) 5/7 (d) 4/7​

Answer 1

Answer:

${\bf{\green{Given, }}}$

${\bf{\red{cosθ=4/5}}}$

${\bf{\blue{by}}}$${\bf{\pink{using }}}$${\bf{\green{P.T:}}}$

${\bf{\orange{we}}}$${\bf{\blue{get}}}$${\bf{\red{sides}}}$${\bf{\green{3,4,5}}}$

${\bf{\pink{sinθ=3/5}}}$

${\bf{\blue{=>cosecθ/(1+cosθ)}}}$

${\bf{\red{=>cosecθ/(1+4/5)}}}$

${\bf{\blue{=>cosecθ/(9/5)}}}$

${\bf{\pink{=>cosecθ×5/9}}}$

${\bf{\green{=>5/9×1/sinθ}}}$

${\bf{\orange{=>5/9×1/3/5}}}$

${\bf{\blue{=>5/9×5/3}}}$

${\bf{\red{=>25/27}}}$

Answer 2

${\bf{\red{Given, cosθ=4/5}}}$

Therefore, sinθ = 3/5.

Now, cosecθ/(1+cosθ) = 5/3 /(1+ 4/5) = 5/3 × 5/9 = 25/27