ICSE Class 10 Answered
Prove it.
(sinA+secA)sq.+(cosA+cosecA)sq.=(1+secAcosecA)sq.
Asked by jaiswalsindhuli717 | 09 Nov, 2018, 04:12: PM
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, 09:10: PM
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