Question

Find the general solution of the equation: 5 cos² θ + 7 sin² θ = 6.

Answer 1

Answer:

θ=±π/4+2πk,where k is any constant.

Step-by-step explanation:

To find the general solution of the equation: 5 cos² θ + 7 sin² θ = 6

write the given equation in one trigonometric function,by using trigonometric formula's

5(1-sin² θ)+7sin² θ=6

5-5sin² θ+7sin² θ=6

2sin² θ=6-5

2sin² θ=1

sin² θ=1/2

sin θ= ± 1/√2

θ = sin-1(±1/√2)

θ =±π/4

So general solution ofthe given equation is θ=±π/4+2πk,where k is any constant.