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Prove the following identities (1-16) ( cosec x - sin x ) ( sec x - cos x ) ( tan x + cot x ) = 1 plizzzzz

Prove the following identities (1-16)

(cosec x-sin x) (sec x-cos x) (tan x+cot x)=1
 
 
plizzzzz
 

Grade:12

1 Answers

Vikas TU
14149 Points
3 years ago
Dear student 
cos20 cos40 cos60 cos80= 1/16
LHS=
cos20 cos40 1/2 cos80 (cos60 = 1/2)
multiply nd divide by 2
1/4 (2 cos20 cos40 cos80)
1/4 (cos(20+80)+ cos(20-80)) cos40 (2cosa cosb= cos(a+b) + cos(a-b))
1/4 (cos(-60)+ cos(100)) cos40
1/4(1/2 + cos100)cos40
1/8 cos40+ 1/4 (cos40 cos100)
multiplt nd divide by 2
2/2(1/8 cos40) + 1/8(2 cos40 cos100)
1/8 cos40+ 1/8 (cos140+ cos(-60)) (2cosa cosb= cos(a+b) cos(a-b))
1/8 cos40+ 1/8 cos140 + 1/16 (cos60= 1/2)
1/8(cos40+cos140) + 1/16
1/8(2 cos90 cos(-50)) + 1/16 (as above identity)
cos90= 0
1/16
= r.h.s

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