Question

Sin theta plus cos theta plus one multiplied by sin theta minus cos theta plus one multiplied by sec theta cosec theta =2

Answer 1

( sinA + cosA + 1 ) ( sinA - cosA + 1 ) ( secA cosecA ) = 2



LHS ,

= > ( sinA + cosA + 1 ) ( sinA - cosA + 1 ) ( secA cosecA )


= > { ( sinA + 1 + cosA ) ( sinA + 1 - cosA ) } ( secA cosecA )


= > { ( sin²A + 1 + 2sinA - cos²A ) } ( secA cosec A )


= > ( sin²A + 2sinA + 1 - cos²A ) ( secA cosecA )


= > ( sin²A + 2sinA + sin²A ) ( secA cosecA )


= > 2sinA ( sinA + 1 ) ( secA cosecA )


= > ( sinA + 1 ) ( 2 sinA ) ( secA cosecA )


$= > ( sinA + 1 ) ( 2 \times \frac{1}{cosecA} ) ( secA cosecA ) \\ \\ \\ \\ = > ( sinA + 1 ) ( 2 \times \frac{1}{cosecA } \times secA \times cosecA ) \\ \\ \\ \\ = > ( sinA + 1 ) ( 2 secA) \\ \\ \\ \\ = > ( sinA \times 2 secA ) + 2secA \\ \\ \\ \\ = > 2 \times tanA +2 secA \\ \\ \\ \\ = > 2(tanA + secA)$





Please check your question.