Question

the value of sina =8/17 then find the value of secacos a+cos a sin a​

Answer 1

Answer:

Answer is given below....

Step-by-step explanation:

$\sin A=\frac{8}{17}$

This indicates that the ratio of the opposite of A to the hypotenuse is 8:17. Let the opposite be 8x and hypotenuse be 17x.

Then, adjacent of A (according to Pythagoras' Theorem)

$=\sqrt{(17x)^2-(8x)^2}\\=\sqrt{289x^2-64x^2}\\=\sqrt{225x^2}\\=15x$

So, then,

$\sec A\cos A+\cos A\sin A\\=\frac{1}{\cos A}*\cos A+\cos A\sin A\\=1+\cos A\sin A\\=1+\frac{Adjacent}{Hypotenuse}*\frac{8}{17}\\\\=1+\frac{15x}{17x}*\frac{8}{17}\\\\=1+\frac{120}{289}\\\\=\frac{289+120}{289}\\\\=\frac{409}{289}$

Hope it helps!

<3