Question

If sec thetha=5/4. Evaluate 4tan theta-5cos thetha/sec thetha+4cot thetha

Answer 1

Heya !!!




Sec theta = 5/4 =H/B





H = 5 and B = 4





By Pythagoras theroem,





(H)² = ( B)² + (P)²




( P)² = ( H)² - (B)²





(P)² = (5)² - (4)²





P² = 25 - 16




P = root 9 = 3




Therefore,




Tan theta = P/B = 3/4




Cos theta = B/H = 4/5




Cot theta = B/P = 4/3



And,



Sec theta = H/B = 5/4





---------------------------------------------------





4 × Tan theta - 5 × Cos theta

———————————————

Sec theta + 4 × Cot theta






4 × 3/4 - 5 × 4/5

—————————.

5/4 + 4 × 4/3







=> 3 - 4 / 5/4 + 16 /3






-1
—————

15 + 64/12






=> -1/79/12





=> -1/79 × 1/12





=> - 1/948

Answer 2

Answer:

Step-by-step explanation:

Since, $sec{\theta}=\frac{5}{4}$, then using the pythagoras theorem,

$tan{\theta}=\frac{3}{4}$, $cot{\theta}=\frac{4}{3}$, $cos{\theta}=\frac{4}{5}$

Then the value of $\frac{4tan{\theta}-5cos{\theta}}{sec{\theta}+4cot{\theta}}=\frac{4(\frac{4}{3})-5(\frac{4}{5})}{\frac{5}{4}+4(\frac{3}{4})}$

=$\frac{3-4}{\frac{5}{4}+\frac{16}{3}}$

=$\frac{-12}{79}$