13. Prove. 1+ tan 0 a) cos 0+ sin 0 = sec 0 1 b) 1- sec 0 1+ sec 0 1 = -2 cot? 0 ,2 c) cos 20- cos 0= sin? 0 – sin? 20

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Chapter2: Second-order Linear Odes
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13. Prove.
1+ tan O
a)
cos 0+ sin O
sec 0
d) sin (7 + x)+cos
- x + tan
+x+
=-cotx
1
b)
1- sec 0
-2 cot? 0
sin (T -x)cos (7+x) tan(27 – x)
e)
1+ sec 0
= sin“ x-
sin x
sec
+x csc
- x cot
c) cos² 20– cos? 0 = sin? 0 – sin² 20
f) cos (x+ y)cos (x- y)= cos² x+ cos² y-1
Transcribed Image Text:13. Prove. 1+ tan O a) cos 0+ sin O sec 0 d) sin (7 + x)+cos - x + tan +x+ =-cotx 1 b) 1- sec 0 -2 cot? 0 sin (T -x)cos (7+x) tan(27 – x) e) 1+ sec 0 = sin“ x- sin x sec +x csc - x cot c) cos² 20– cos? 0 = sin? 0 – sin² 20 f) cos (x+ y)cos (x- y)= cos² x+ cos² y-1
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