Question

N + Which is the exact value of sin 75°? (1 point) V6- V6 +12 Voſ 16 +2 N I + Which statement is true? (1 point) cos? 290 - 1- cos 580 tan 34° = 2tan 17° 1-tan? 17° Evaluate cos Evaluate 2 (1 point) 2+2 4 02-22

Answer 1

To Find value of sin 75° use the following identity =) sina = cos(90° ). sin 75= Cos (90-150) = cos 150 Cos 15° = write los 150 as cos (30) => Cos (30) using the half angle identity cos (+2) = 1+ lost 1. it cos (30) use the following trivial identity Cos (36) = 53 2 > Jetuvos ~ Vestue 4. - 0.9659 = 0.9659 :. The option is so the 2 which statements is true. tan 34 = 2 tan 17° i-tan? 17° use the following identity: 2 tantx) - tan (2x) - tan? (x) - :.= 2 tan (17) 1- tan² (170) = tan (2, 17) = tan (2.170) ) tan (34) The 4th option tan 34 = 24 o atan 17 is true 1-tan² z

(3) Given cos? (II) use the following identity: Cos2(x) = It Cos (2) Cosa (7) = 14 Cos (27) ( Multiply 2. I 2 = 77 - - It los 7 use the following trivial identity: cos (I) = se & + 2 + -) 1 = 1 0 2 2 키를 이를 2 Apply the fraction rule & = 1.2+52 b - 2+52 z for 2+52 take a common - Seti Ca - Set 2.se

Rationalize 2+1 2a 52 Multiply the conjugate a = 2 (2+1) cancel the like terms - f (52+1) - 2+2 the+Dre=2+52 52.250 = 4