we have the left hand side as
we multiply numerator and denominator by
now using identity
hence proved ,
8. (a) (5pt) Prove the identity: cscx -cos x=sec x . sin'x 4 and tan θ<0 (b) (5pt) Find cos θ , if sin θ 8. (a) (5pt) Prove the identity: cscx -cos x=sec x . sin'x 4 and tan θ
DETAILS MCKTRIG8 5.3.051. (-/1 Points] Prove the following identity. sin 30 -3 sine 4 sino We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30 = sin + sin...
Establish the identity. 1 - sin e 1+ sin e = (sec - tan e) Starting with the right side, which shows the key steps in establishing the identity? 1 + sin e 1 1 - sin 0 OA. (sec 0 - tan 9)2 = sec? -tan?= (1 - sin 02 1- sin 1 - sine ОВ. 2 sin 0 sine (1 - sin oy? (sec - tan )2 = cos? e cos2 e O c. 1 - sin (1...
Verily the identity sec 0-cos 0-tan 0sin 0 To verily the identity, start with the more complicated side and transfomit to look ke the other side Choose the comect transformations and transform the expression at each step sec 0-cos 0 -cos0 tan Osin 0 Verify the identity sec 0-cos 0= tan 0 sin 0 To verify the identity, start with the more complicated side and transfo sec 0- cos 0 cos 0 Factor out the greatest common factor Apply the...
Find sin , cos , and tan - O A. sino= _ . cosO=- , tan 0= - 13 O B. sino= - ], COSO = 3, tan o=1/3 o c. sino=- , coso - ., tan og OD. sino - 13. COSO = 1, tan 0=13 Find the exact value of sin 510º. O B. v O A. OC. O D. Find the exact value of tan 111. OA OB. Z OD. 13 OC. 2 Suppose that there is...
(a) If sec 0 = 5, find (a) tan 6 (b) cos (90° – 0) (c) sino (b) Prove by using Pythagorean identities sin? 6 - cos2 = 2 sin2 0-1
establish the identity Establish the identity. cos 0 sin = sin 0 - cos 0 - 1- tan 0 - 1- coto Write the left side in terms of sine and cosine. cos 0 sin o -1- Write each term from the previous step as one fraction. cos?o sin 0 - cos 0 (List the terms in the same order as they appear in the original list.) Add the fractions from the previous step. (Do not simplify.) cos 0 -...
Establish the identity. 1 - sec 0 1 + sec cos 0-1 cos + 1 1 Which of the following four statements shows the key steps in establishing the identity? ОА. 1 cos + 1 1 - 1 - sec 0 cos e cos Ꮎ cos 0-1 1 + sec 0 1 1 + cos 0-1 cos 0+1 cos o cos e B. 1 cos + 1 1 + 1 - sec 0 cos o cos Ꮎ cos 0-1 1...
QUESTION 3 Using the appropriate identity below, find the value of cos cos( 5 – B).ca (Angles are measured in radians.) Formula Sheet Sum & Difference Identities Half Angle Formulas CON 1 + cos(0) 2 cos(0) 2 sin - + cos(a+B) cos(a) cos(8) – sin(a) sin() cos(a-B) cos(a) cos(8) + sin(a) sin() sin(a+b) sin(a) cos(8) + cos(a) sin(8) sin(a -B) sin(a) cow (8) - cos(a) sin() tan(a)tan(B) tan(a+B) 1 - tan(a)tan (8) tan(a)-tan(8) tan(a-) 1+tan(Q) tan() Power Reduction Formulas tan...
1-17 u ule exact value of the expression 1) cos? 30+ cos? 60 2) cot 45-tan 45 5-6 Use the given information to find the exact value 3) sin? 53 + cos2 53 4) cot 20 -tan 20 5) sin = , where is in quadrant 1. Find tan 6) tan 0 = - , where is in quadrant 4. Find sec 7-12 Verify the identity 7) tan sin cos 0 = sin? 8) tane = sine 9) tancos? +...