Question

answer this plzz....

Answer 1

i) Dividing both sides by 41, (9/41)*cos(A) + (40/41)*sin(A) = 1 

ii) This is of the form, cos(A)*cos(B) + sin(A)*sin(B) = 1, where cos(B) = 9/41 and sin(B) = 40/41 

iii) So, cos(A - B) = 1 
==> A - B = 2nπ 
Hence A = 2nπ + B 

iv) So, cos(A) = cos(2nπ + B) = cos(B) = 9/41 
csc(A) = csc(2nπ + B) = csc(B) = 41/40

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OR
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9 * cos(a) + 40 * sin(a) = 41 
sqrt(9^2 + 40^2) * (cos(a) * 9/sqrt(9^2 + 40^2) + sin(a) * 40 / sqrt(9^2 + 40^2)) = 41 
41 * (cos(a) * 9/41 + sin(a) * 40/41) = 41 
cos(a) * (9/41) + sin(a) * (40/41) = 1 

sin(b) = 9/41 
cos(b) = 40/41 

cos(a) * sin(b) + sin(a) * cos(b) = 1 
sin(a + b) = 1 
sin(a + b) = sin(pi/2) 
a + b = pi/2 
a = pi/2 - b 

cos(a) => 
cos(pi/2)cos(b) + sin(pi/2)sin(b) => 
sin(b) => 
9/41 

csc(a) => 
1/sin(a) => 
1/sin(pi/2 - b) => 
1 / (sin(pi/2)cos(b) - sin(b)cos(pi/2)) => 
1 / cos(b) => 
1 / (40 / 41) => 
41/40

ℍᝪℙℰ ⅈᝨ ℍℰℒℙՏ ℽᝪႮ 

Answer 2

here is your answer :-
) Dividing both sides by 41, (9/41)*cos(A) + (40/41)*sin(A) = 1 

ii) This is of the form, cos(A)*cos(B) + sin(A)*sin(B) = 1, where cos(B) = 9/41 and sin(B) = 40/41 

iii) So, cos(A - B) = 1 
==> A - B = 2nπ 
Hence A = 2nπ + B 

iv) So, cos(A) = cos(2nπ + B) = cos(B) = 9/41 
csc(A) = csc(2nπ + B) = csc(B) = 41/40