Question

If tan A=5by12
Find the value of sin A+ cosA) secA​

Answer 1

Answer:

17/12

Step-by-step explanation:

$Tan A = {\Large\frac{5}{12}}=\Large\frac{P}{B}$

Find 3rd side by using Pythagorous theorem:

$\implies$ $H^{2}=P^{2}+B^{2}$

$\implies$ $H^{2}=5^{12}+12^{2}$

$\implies$ $H=\sqrt{169}$

$\implies$ $\boxed{H=13}$

$SinA={\Large\frac{P}{H}}={\Large\frac{5}{13}}$

$CosA={\Large\frac{B}{H}}=\Large\frac{12}{13}$

$SecA={\Large\frac{H}{B}}=\Large\frac{13}{12}$

Now substitute these values in the given equation :

$\implies$ $(SinA+CosA)×SecA$

$\implies$ $({\Large\frac{5}{13}}+\Large\frac{12}{13})×\Large\frac{13}{12}$

$\implies$ $({\Large\frac{17}{13}})×\Large\frac{13}{12}$

$\implies$ $\large\boxed{\frac{17}{12}}$

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