cos A - sin a+1 /cos a + sin a -1= cosec a + cot a
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Secondary School Math 5 points
Cos A - sin A +1 ÷ COS A + sin A - 1
= cosec A + cot A,
Ask for details Follow Report by Super60hema 25.09.2019
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abhi178
abhi178 Genius
we have to prove : (cosA - sinA + 1)/(cosA + sinA - 1) = cosecA + cotA.
LHS = (cosA - sinA + 1)/(cosA + sinA - 1)
= (cosA - sinA + 1)(cosA - sinA + 1)/(cosA + sinA - 1)(cosA - sinA + 1)
= (cosA - sinA + 1)²/(cos²A - sin²A - 1 + 2sinA)
= (cosA - sinA + 1)²/(-2sin²A + 2sinA)
= (cos²A + sin²A - 2sinA.cosA + 2cosA - 2sinA + 1)/2sinA(1 - sinA)
= (2 - 2sinA.cosA + 2cosA - 2sinA)/2sinA(1 - sinA)
= (1 - sinA)(1 + cosA)/sinA(1 - sinA)
= (1 + cosA)/sinA
= cosecA + cotA = RHS
Cos A- sin A+1/cos A+ sin A-1=cosec A+cot A