Question 8:

Find the general solution of the equation sec² 2x = 1 – tan 2x

Answer

sec²2x = 1- tan 2x

⇒ 1 + tan² 2x= 1 = 1 – tan 2x

⇒ tan² 2x + tan 2x = 0

⇒ tan 2x(tan 2x + 1) = 0

⇒tan 2x = 0                       or                    tan 2x + 1 = 0

Now, tan 2x = 0

⇒ tan 2x = tan 0

⇒ 2x = nπ + 0, where n ∈ Z

⇒ x = nπ/2, where n ∈ Z

tan 2x + 1 = 0

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