The equation tan^2 x+1=sec^2 x is an identity true or false Question The equation tan^2 x+1=sec^2 x is an identity true or false in progress 0 Math Charlie 1 week 2021-09-11T02:18:33+00:00 2021-09-11T02:18:33+00:00 1 Answer 0

## Answers ( )

Answer:tan²x + 1 = sec²x is identity

Step-by-step explanation:* Lets explain how to find this identity

∵ sin²x + cos²x = 1 ⇒ identity

– Divide both sides by cos²x

∵ sin x ÷ cos x = tan x

∴ sin²x ÷ cos²x = tan²x

– Lets find the second term

∵ cos²x ÷ cos²x = 1

– Remember that the inverse of cos x is sec x

∵ sec x = 1/cos x

∴ sec²x = 1/cos²x

– Lets write the equation

∴ tan²x + 1 = 1/cos²x

∵ 1/cos²x = sec²x

∴ than²x + 1 = sec²x

– So we use the first identity sin²x + cos²x = 1 to prove that

tan²x + 1 = sec²x

∴ tan²x + 1 = sec²x is identity