Question

If 5 sec -4tan a=3cosec a then find the value of 27 cot a/ 5tan a -4sec a

Answer 1

$\textbf{Given:}$

$\bf\,5\,secA-4\,tanA=3\,cosecA$

$\textbf{To find:}$

$\textbf{The value of \bf\dfrac{27\,cotA}{5\,cotA-4\,secA} }$

$\textbf{Solution:}$

$\boxed{\begin{minipage}{11cm} \text{consider}\\\\5\,secA-4\,tanA=3\,cosecA\\\\\text{Squaring on bothisdes, we get}\\\\25\,sec^2A+16\,tan^2A-40\,secA\,tanA=9\,cosec^2A\\\\25(1+tan^2A+16(sec^2A-1)-40\,secA\,tanA=9\,cosec^2A\\\\25\,tan^2A+16\,sec^2A+9-40\,secA\,tanA=9\,cosec^2A\\\\25\,tan^2A+16\,sec^2A-40\,secA\,tanA=9\,cosec^2A-9\\\\25\,tan^2A+16\,sec^2A-40\,secA\,tanA=9(cosec^2A-1)\\\\25\,tan^2A+16\,sec^2A-40\,secA\,tanA=9\,cot^2A\\\\(5\,tanA-16\,secA)^2=9\,cot^2A\\\\\text{Taking square root on bothsides, we get}\\\\5\,tanA-16\,secA=3\,cotA\\\\\implies\,9(5\,tanA-16\,secA)=27\,cotA\\\\\implies\bf\dfrac{27\,cotA}{5\,tanA-16\,secA}=9 \end{minipage}}$

$\textbf{Answer:}$

$\therefore\textbf{The value of \bf\dfrac{27\,cotA}{5\,cotA-4\,secA} is 9}$

Find more:

Prove that (tanA + secA ÷ cosecA + cotA)(tanA - secA ÷ cosecA - cotA) = 2(tanA×cosecA - cotA×secA)

https://brainly.in/question/8676527

(cotA/cotA-cot3A)-(tanA/tan3A-tanA)=1

https://brainly.in/question/9805113

Answer 2

Answer:

Step-by-step explanation: