Question

If cos theta equals to 2 by 3 then find the value of 2 sec squared theta + 2 tan squared theta -7

Answer 1

Hope it will help you

Answer 2

Answer:

2sec²θ + 2tan²θ - 7= 0

Step-by-step explanation:

Given cosθ = 2/3

We have to find the value of 2sec²θ + 2tan²θ - 7

By phythagoras theorem,

3² = (BC)² +2²

(BC)² = 9 - 4

BC = √5

sec²θ = ($\frac{3}{2}$)² = $\frac{9}{4}$

2sec²θ = 2× $\frac{9}{4}$= $\frac{9}{2}$

tanθ = ($\frac{\sqrt{5} }{2}$)

tan²θ = $\frac{5}{4}$

Now, 2sec²θ + 2tan²θ - 7=

$\frac{9}{2} +2(\frac{5}{4} )-7\\=\frac{9}{2}+\frac{5}{2} -\frac{7}{1} \\=\frac{9+5-14}{2} \\=\frac{14-14}{2} =\frac{0}{2} =0$

Therefore, 2sec²θ + 2tan²θ - 7=0