Analytic Trigonometry Discussion Assignment

Analytic Trigonometry Discussion Assignment

Fundamental Trigonometric Identities

For questions 433 to 442, prove that the given equation is an identity. Refer to

the following table of fundamental identities, as needed.

Fundamental Trigonometric Identities

Note: The convenient notation for exponents on trig functions, (sin )

2 = sin

2

,

will be used throughout this book.

A word of advice: Not only should you memorize the identities in the preceding

table but also own them. That is, they should be an instinctive part of your

mathematical knowledge.

433. sin x cot x = cos x

434. sin x(csc x – sin x) = cos

2 x

435. (1 sin x)(1 sin(–x)) = cos

2 x

436. tan

2 x csc

2 x – tan2 x = 1

437. tan x(csc x cot x) = sec x 1

438. = cot x

439. = csc x

440. = cos x

441. (sin x cos x)

2 = 1 2 sin x cos x

442. sec

4 x – tan

4 x = sec

2 x tan

2 x

Analytic Trigonometry Discussion Assignment

Sum and Difference Identities

For questions 443 to 455, prove that the given equation is an identity. Refer to

the following sum and difference identities, as needed.

443. sin(x 2π) = sin x

444. cos(x 2π) = cos x

445. tan(x π) = tan x

446. cos (cos x – sin x)

447. sin(α β) sin(α – β) = sin

2 α – sin

2 β

448. tan

449. sin(2 ) = 2 sin cos

450. cos(2 )=2 cos

2 – l

451. sin(4x) = 4 sin x cos x(1– 2 sin

2 x)

452. = cot

2 x – 1

453.

454. tan(2 ) =

455. tan(2x) =

Double- and Half-Angle Identities

For questions 456 to 458, prove the given equation is an identity. Refer to the

following double- and half-angle identities, as needed.

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