Question

if cosec theta -cot theta=1/4 find the value of cosec theta + cot theta

Answer 1

Answer:

$\implies cosec\theta+cot\theta = 4$

Step-by-step explanation:

$Given \\cosec\theta-cot\theta=\frac{1}{4}---(1)$

$We \: know \: the \: \\Trigonometric \: identity :\\\boxed{cosec^{2}\theta -cot^{2}\theta = 1}$

$(cosec\theta+cot\theta)(cosec\theta-cot\theta)=1$

$By \: algebraic \: identity :\\\boxed {x^{2}-y^{2}=(x+y)(x-y)}$

$\implies \frac{1}{4}(cosec\theta+cot\theta)=1\:[ from\: (1)]$

$\implies cosec\theta+cot\theta = 4$

Therefore,

$\implies cosec\theta+cot\theta = 4$

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Answer 2

answer is

4 .........,..........