Question

If cosecx+cotx=2.50 find cosecx =?​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$\displaystyle \: cosecx + cotx \: = 2.5 \: \: ...........(1)$

TO DETERMINE

$cosecx$

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric identity that

${cosec}^{2} x - {cot}^{2} x = 1$

EVALUATION

Here

${cosec}^{2} x - {cot}^{2} x = 1$

$\implies(cosecx + cotx)(cosecx - cotx) = 1$

$\implies2.5 \times (cosecx - cotx) = 1$

$\displaystyle \: \implies(cosecx - cotx) = \frac{1}{2.5}$

$\displaystyle \: \implies(cosecx - cotx) = \frac{2}{5} \:$

$\displaystyle \: \implies(cosecx - cotx) = 0.4 \: ......(2)$

Equation (1) + Equation (2) gives

$2cosecx = 2.9$

$\therefore \: cosecx \: = 1.45$