# Analytic Trigonometry Discussion Assignment

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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