Complete the identify. csc (alpha - beta) = ? csc alpha, sec beta - sec alpha cs

Question

Complete the identify. csc (alpha - beta) = ? csc alpha, sec beta - sec alpha csc beta sec alpha sec beta/tan alpha - tan beta sec alpha sec beta/tan alpha tan beta - 1 csc alpha - csc beta Find the exact value of the expression. cos (5 pi/18) cos (pi/9) + sin (5 pi/18) sin (pi/9) 1/4 Squareroot 3/2 1/2 1 Experss the product as a sum containing only sines or cosines. sin theta/2 cos 9 theta/2 1/2 [sin (5 theta) - sin (4 theta)] 1/2 [cos 95 theta) + sin (4 theta)] 1/4 sin cos (9 theta) 1/4 [cos (10 theta) - sin (8 theta)] Express the product as a sum containing only sines or cosines. sin (3 theta) cos (4 theta) 1/2 [sin (7 theta) - sin theta] 1/2 [xos (7 theta) + sin theta] sin cos (12 theta^2) 1/2 [cos (7 theta) - cos theta]

Explanation / Answer

Csc(alpha-beta)=1/sin(alpha-beta)=1/(sin alpha cos beta-cos alpha sin beta)

Dividing both top and bottom by cos alpha cos beta

=sec alpha sec beta/(tan alpha -tan beta)

2.cos(5pi/18)cos(pi/9)+sin(5pi/18)sin(pi/9)

Cos(5pi/18-pi/9)=cos(pi/6)=sqrt3/2

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