Q. (cosecA – sinA)(secA – cosA)(tanA + cotA) किसके बराबर है?
✅ Correct Answer: (C)
1
Explanation: = (1/sinA - sinA)(1/cosA - cosA)(sinA/cosA + cosA/sinA)
= (1-sin^2A)/sinA x (1-cos^2A)/cosA x (sin^2A + cos^2A)/sinA cosA
= (1-sin^2A)(1-cos^2A)(sin^2A + cos^2A) / sin^2A cos^2A
= 1-sin^2A-cos^2A+sin^2A cos^2A / sin^2A cos^2A
= 1-(sin^2A+cos^2A)+sin^2A cos^2A / sin^2A cos^2A
= 0 +sin^2A cos^2A / sin^2A cos^2A
= sin^2A cos^2A / sin^2A cos^2A
= 1
Explanation by: Chandan Das
= (1/sinA - sinA)(1/cosA - cosA)(sinA/cosA + cosA/sinA)
= (1-sin^2A)/sinA x (1-cos^2A)/cosA x (sin^2A + cos^2A)/sinA cosA
= (1-sin^2A)(1-cos^2A)(sin^2A + cos^2A) / sin^2A cos^2A
= 1-sin^2A-cos^2A+sin^2A cos^2A / sin^2A cos^2A
= 1-(sin^2A+cos^2A)+sin^2A cos^2A / sin^2A cos^2A
= 0 +sin^2A cos^2A / sin^2A cos^2A
= sin^2A cos^2A / sin^2A cos^2A
= 1
= (1-sin^2A)/sinA x (1-cos^2A)/cosA x (sin^2A + cos^2A)/sinA cosA
= (1-sin^2A)(1-cos^2A)(sin^2A + cos^2A) / sin^2A cos^2A
= 1-sin^2A-cos^2A+sin^2A cos^2A / sin^2A cos^2A
= 1-(sin^2A+cos^2A)+sin^2A cos^2A / sin^2A cos^2A
= 0 +sin^2A cos^2A / sin^2A cos^2A
= sin^2A cos^2A / sin^2A cos^2A
= 1