proof that (1+cot a _cosec a )(1+tan a+sec a ) = 2
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Solve : (1+cotA−cosecA)(1+tanA+secA)=2
Step-by-step explanation:
( 1 + cot A - cosec A ) ( 1+ tan A + sec A )
= ( 1+ cos A / sin A - 1/ sinA ) ( sinA + cosA + 1/ cosA
= (sin + cosA)² -1² / sinA cosA. [(a+ b) ( a- b)] = a² - b²
= sin²A + cot² A + 2 sinA cosA - 1 / sinA cotA
= 1 + 2 sinA cosA - 1 / sinA cosA ( sin²A + cos²A = 1 )
= 2 sinA cosA / sinA cos A
= 2 = RHS
LHS = RHS
Hence, proved
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