Assume cos(x) +5sin(x) 235 and 6cos(x)+sin(x)225 Find t

Assume cos(x) +5sin(x)= 23/5

and

6cos(x)+sin(x)=22/5

Find the exact numeric value of sec(x) and find the exact numeric value of tan(x).

Solution

cos(x) +5sin(x) = 23/5 ———— (1)

6cos(x)+sin(x) = 22/5 ————– (2)

6 * (1) – (2)==> 6cos(x) +30sin(x) – {6cos(x)+sin(x)} = 138/5 – 22/5

==> 29sinx = 116/5

==> sinx = █████████████ = ██████

==&██████; ███████ = ██████(███ ████████████████) = ██████(██ &#███████; (█████)███)

==&██; ███████ = █████████(███████)

==&████; ███████████ = ██████

██████ = █████████ = ███(████)

==&███; ██████████ = ██████

███████ = ████████████████████ = (█████)██(█████)

==&████; █████████ = ███████