Question

if 5tan theta is 12 then find the value of 5sectheta +12cot theta /13sin theta + 5 cosec theta​

Answer 1

Answer:

given

5tan○= 12

tan○=12/5. (where 12 is opp. and 5 is adj.)

therfore using py. th. hyp. =13

sec○=13/5. (sec○=1/cos○)

cot○=5/12. (cot○=1/tan○)

sin ○= 12/13

cosec○=13/12

substituting these values....,

13+5/144+60/12

18/17...........answer

hope it helps

pls mark as brainliest

Answer 2

$\frac{5sec\theta+12cot\theta}{13sin\theta+5cosec\theta}=\frac{216}{209}$

Step-by-step explanation:

$5tan\theta=12$

$tan\theta=\frac{12}{5}$

$cot\theta=\frac{1}{tan\theta}$

Using the  formula

$cot\theta=\frac{5}{12}$

$sec\theta=\sqrt{1+tan^2\theta}$

Substitute the values

$sec\theta=\sqrt{1+(\frac{12}{5})^2}$

$sec\theta=\sqrt{1+\frac{144}{25}}=\sqrt{\frac{25+144}{25}}=\sqrt{\frac{169}{25}}$

$sec\theta=\frac{13}{5}$

$cosec^2\theta=1+cot^2\theta$

Substitute the values

$cosec^2\theta=1+(\frac{5}{12})^2=1+\frac{25}{144}=\frac{144+25}{144}=\frac{169}{144}$

$cosec\theta=\sqrt{\frac{169}{144}}=\frac{13}{12}$

$sin\theta=\frac{1}{sec\theta}=\frac{12}{13}$

$\frac{5sec\theta+12cot\theta}{13sin\theta+5cosec\theta}=\frac{5\times \frac{13}{5}+12\times \frac{5}{12}}{13\times \frac{12}{13}+5\times \frac{13}{12}}$

$\frac{5sec\theta+12cot\theta}{13sin\theta+5cosec\theta}=\frac{13+5}{12+\frac{65}{12}}=\frac{18}{\frac{144+65}{12}}=\frac{18\times 12}{209}=\frac{216}{209}$

#Learn more:

https://brainly.in/question/2230871:Answered by Sibbi