Question

Plz anyone help me with this question......​

Answer 1

Question -

To prove :

1/sinA + cos A + 1/sin A - cos A = 2 sinA/1 - 2 cos² A

Solution :

LHS :

1/sinA + cos A + 1/sin A - 2 cos² A

Taking LCM ;

=> ( sinA - cos A ) + ( sin A + cos A )/ ( sin A + cos A )( sin A - cos A )

=> { 2 sin A }/{ ( sin A + cos A )( sin A - cos A ) }

=> { 2 sin A }/{ sin²A - sin A cos A + sin A cos A - cos² A }

=> { 2 sin A }/{ sin² A - cos ²A }

=> { 2 sin A }/{ 1 - cos² A - cos ² A }

=> { 2 sin A }/{ 1 - 2 cos ² A }

Hence Proved

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