(1-cosectheta)(1-sectheta)(1+cosectheta)(1+costheta)=costheta
Sushma Harish , 9 Years ago
Grade 10
Trigonometry> (1-cosectheta)(1-sectheta)(1+cosectheta)(...
1 AnswersSreevignesh
I can't insert theta... So I am using x instead of theta
(1-cosec x ) ( 1-sec x) (1+cosec x ) ( 1+cos x)
= (1-cosec x ) ( 1+ cosec x) (1- 1/cos x) ( 1+ cos x)
= (1 - cosec ² x) [ ( cos x -1 )/ cos x] ( 1+ cos x ). [ using (a+b)( a- b)= a²+b²
and taking LCM]
= (- cot ² x) × [( cos ²x -1 ) /cos x]. [ multiply using ( a+b) ( a- b)=a²+b²
And 1+ cot ²x = cosec ²x]
= (- cos ²x )/(sin ²x) × (- sin ²x)/ cos x. [ cot x = cos x /sin x]
= cos x [ sin ²x+ cos ²x =1 ]
On cancelling , sin²x will be removed
Two - signs will become + and
Only one cos x will be there
Hence it is proved
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