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ICSE Class 10 Answered

Prove it. (sinA+secA)sq.+(cosA+cosecA)sq.=(1+secAcosecA)sq.
Asked by jaiswalsindhuli717 | 09 Nov, 2018, 16:12: PM
answered-by-expert Expert Answer
(sin A + sec A)² + (cos A + cosec A)² 
=  (sin A + 1/cos A)² + (cos A + 1/ sinA)²
=   (sin A cos A  + 1)² / cos² A    +  (sinA cosA + 1)² / sin² A
= [ sin A cos A + 1]² [ 1/cos² A + 1/sin² A ] 
= [  sin A cos A + 1]² [ cos² A + sin² A ] / [sin²A cos² A ]
= [ sin A cos A + 1 ]²  /  [sin²A cos² A ]
= [ (sin A cos A + 1) / (sin A cos A )]²
=  (1 + 1/sin A x 1/cos A)² 
= (1 + sec A cosec A)²
Answered by Arun | 09 Nov, 2018, 21:10: PM

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