sec^2xtanx=2tanx

Answer 1

The trigonometric equation is sec² (x) tan x = 2tan(x).

tan x[ sec² (x) - 2] = 0

⇒tan x = 0 and sec² (x) - 2 = 0.

tan x = 0.

tan x = tan 0.

The genaral solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

⇒ x = nπ + 0

x = nπ.n = 0,1,2........

sec² (x) - 2 = 0

sec² (x) = 2

Using reciprocal identity : sec² x = 1/cos² x .

(1/cos² x) = 2

1 = 2cos² x

cos² x = 1/2

cos x = ±1/√2.

cos x = 1/√2  and  cos x = - 1/√2.

cos (x) = 1/√2.

cos (x) = cos(π/4)

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

x = 2nπ ± π/4 : n = 0,1,2........

os (x) = -1/√2.

cos (x) = cos(3π/4)

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

x = 2nπ ± 3π/4 : n = 0,1,2........