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Unformatted text preview: (Chapter 1: Review) 1.51
Now, 1 cos
sign as sin
= 0 for all real , and tan 2 has the same (can you see why?), so … 1 cos
sin To get the third formula, use the numerator’s (instead of the
denominator’s) trig conjugate, 1 + cos , when multiplying into the
numerator and the denominator of the radicand in the first few steps. GROUP 6: PRODUCT-TO-SUM IDENTITIES
These can be verified from right-to-left using the Sum and Difference Identities.
The Identities: 1
cos u cos v =
sin u cos v =
cos u sin v =
sin u sin v = cos u v ( ) cos u + v ( ) ( ) ( ) ( ) ( ) cos u v + cos u + v ( ) ( ) sin u + v + sin u v
sin u + v sin u v GROUP 7: SUM-TO-PRODUCT IDENTITIES
These can be verified from right-to-left using the Product-To-Sum Identities.
sin x + sin y = 2sin xy
2 sin x sin y = 2cos x+ y
2 cos x + cos y = 2cos x+ y
2 cos x cos y = 2 sin x+ y
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.
- Fall '10