Question

if cos theta equal to 2 by 3 then find the value of 2 sec square theta + 2 10 squared theta minus 7

Answer 1

Answer:

Step-by-step explanation:

I suppose the equation is 2(secθ)^2 + (tanθ)^2 - 7.

cosθ=2/3 (Given)

So to find the value of secθ we can use secθ = 1/(cosθ)

secθ = 1/(2/3) = 3/2

We can also use the theorem (tanθ)^2 = (secθ)^2 - 1

So now the equation is 2(secθ)^2 + [(secθ)^2 - 1] -  7

By solving this we get 3(secθ)^2 - 8

By putting the value of secθ we get [3*(4/9)] - 8 = (4/3) - 8 = -20/3