Question

If cosec teta – cot teta= 3 then cosec teta + cot teta ?​

Answer 1

$\huge\rm\underline\purple{GIVEN:}$

• $\large\rm{cosec\theta-cot\theta\:=\:3}$

$\huge\rm\underline\purple{TO\:FIND:}$

• $\large\rm{cosec\theta+cot\theta}$

$\huge\rm\underline\purple{SOLUTION:}$

$\large\rm{Cosec\theta-Cot\theta\:=\:3----eq(1)}$

$\large\rm\bold{\boxed{Cosec^2\theta-Cot^2\theta\:=\:1}}$

$\large\rm\bold{\boxed{a^2-b^2\:=\:(a+b)(a-b)}}$

$\large\rm{\implies{(Cosec\theta+Cot\theta)(Cosec\theta-Cot\theta)\:=\:1}}$

$\large\rm{\implies{(Cosec\theta+Cot\theta)(3)\:=\:1\:(from\:eq(1))}}$

$\large\rm{\implies{(Cosec\theta+Cot\theta)\:=\:\frac{1}{3}}}$

$\large\rm{\therefore{Cosec\theta+Cot\theta\:=\:\frac{1}{3}}}$