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Prore each of the following identities: (ii) (1+cot 0)sin 0 1 1 (1) (1-cos 0)cosec o=1 rie-1)cot 0 1 (ii) (sec20-1)(cosec'0-

Prore each of the following identities: (ii) (1+cot 0)sin 0 1 1 (1) (1-cos 0)cosec o=1 rie-1)cot 0 1 (ii) (sec20-1)(cosec'0-

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Guel Prove each of the identities: (ii) cosec cos 0-cot 0) =1 Also, sin'B sin'A cos B-cos' A sin' B (d s0 - 1) V s03-S0 (V s0 - ) cos B cos' A cos B cos A EXERCISE 13A (ii) (1 + cot 0) sin20 = 1 (ii) (sec20- 1)(cosec20- 1) = 1 1 ) (1- cos 0)cosec 0 =1 I = 0100(1-0,20s) (1) 7 (ii) (1- cos 0)sec 0 = tan20 (!!) (1+tan²0) (1+ cot²0) 3. (i) sin20+ (1+ tan?0) =D1 () (1 + cos 0)(1- cos 0)(1+cot e) = 1 (ii) tan20- 1. +0, soɔ (m) (1+cot 0) = 2 sec2e 6. 1+ sin 0) (1- sin 0) 991 Therefore, the coordinates of the points of trisection c B are (-1, 0) and (-4, 2). Note : We could also have obtained Q by noting tha could have obtained its coordinates using the mid-p Example 9: Find the ratio in which the y-axis c points (5,-6) and (-1,-4). Also find the pointe Solution: Let the ratio be k: 1. Then by the se point which divides AB in the ratio k: 1 are
Transcribed Image Text:Guel Prove each of the identities: (ii) cosec cos 0-cot 0) =1 Also, sin'B sin'A cos B-cos' A sin' B (d s0 - 1) V s03-S0 (V s0 - ) cos B cos' A cos B cos A EXERCISE 13A (ii) (1 + cot 0) sin20 = 1 (ii) (sec20- 1)(cosec20- 1) = 1 1 ) (1- cos 0)cosec 0 =1 I = 0100(1-0,20s) (1) 7 (ii) (1- cos 0)sec 0 = tan20 (!!) (1+tan²0) (1+ cot²0) 3. (i) sin20+ (1+ tan?0) =D1 () (1 + cos 0)(1- cos 0)(1+cot e) = 1 (ii) tan20- 1. +0, soɔ (m) (1+cot 0) = 2 sec2e 6. 1+ sin 0) (1- sin 0) 991 Therefore, the coordinates of the points of trisection c B are (-1, 0) and (-4, 2). Note : We could also have obtained Q by noting tha could have obtained its coordinates using the mid-p Example 9: Find the ratio in which the y-axis c points (5,-6) and (-1,-4). Also find the pointe Solution: Let the ratio be k: 1. Then by the se point which divides AB in the ratio k: 1 are
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