math 112 - elementary functions homework, due after 2 hours, very easy.

MTH-112 HOMEWORK #4

SECTIONS 7.1, 7.2, AND 7.3

This homework assignment is due in class on Tuesday, August 8th. Please write your answers clearly. You may work with other students if you wish, but you should turn in your own work. Wherever appropriate, your solutions should be fully justified and explained using complete sentences.

(1) Verify each of the following trigonometric identities.

(a) sec x csc x = tan x + cot x

(b) 1 + tan θ

sin θ + cos θ = sec θ

(c) (1 − sin θ)(tan θ + sec θ) = cos(−θ)

(d) (csc x − cot x)2 = 1 − cos x 1 + cos x

(2) For each of the following, either verify the given identity or use a counterexample to show that the given expression is not an identity.

(a) (sin A − cos A)2 = 1 − 2 sin2 A cot A

(b) sec2 x − 1 = cos x

csc x

(c) sin2 θ + cos2 θ + tan2 θ + sec2 θ + cot2 θ + csc2 θ = 3

(d) sin x + cos x + tan x sin x = sec x + cos x tan x

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