Ex 8.1, 9
In triangle ABC, right-angled at B, if tan A = 1/β3, find the value of
sin A cos C + cos A sin C
Given
tan A = 1/β3
(πΊππ π ππππππππ ππ π¨)/(πΊππ π ππ ππππππ ππ π¨) = π/βπ
π΅πΆ/π΄π΅ = 1/β3
Let BC = x
& AB = βπ x
We have to find
sin A cos C + cos A sin C
Putting sin A = 1/2 , cos A = β3/2 , sin C = β3/2 & cos C = 1/2
= (π/π)Γ(π/π)+(βπ/π)Γ(βπ/π)
= 1/4 + (β3 Γ β3)/4
= 1/4 + 3/4
= (1 + 3)/4
= 4/4
= 1
So, sin A cos C + cos A sin C = 1
Ex 8.1, 9
In triangle ABC, right-angled at B, if tan A = 1/β3, find the value of
(ii) cos A cos C β sin A sin C
cos A cos C β sin A sin C
Putting sin A = 1/2 , cos A = β3/2 , sin C = β3/2 & cos C = 1/2
= (βπ/π)Γπ/πβ(π/π)Γ(βπ/π)
= (β3/4)β(β3/4)
= 0
Hence, cos A cos C β sin A sin C = 0

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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