Question

prove that =(cot E - cos E )/(cot E + cos E )= (cosec E -1)/(cosecE+1)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

(cot E - cos E)/(cot E + cos E) = (cosec E - 1)/(cosec E + 1)

Rationalising LHS

(cot E - cos E)/(cot E + cos E) × (cot E - cos E)/(cot E - cos E)

(cot E - cos E)² / (cot E)² - (cos E)²

• (cot A)² - (cos A)² = cot²A .cos²A

cot²E + cos²E - 2.cotE cosE / cot²E .cos²E

1/cos²E + 1/cot²E - 2/cotE cosE

sec²E + tan²E - 2sinE/cos²E

1/cos²E + sin²E/cos²E - 2sinE/cos²E

(1 + sin²E - 2sinE)/cos²E

• cos²A = 1 - sin²A

(1 - sinE)² / 1 - sin²E

(1 - sinE)(1 - sinE) / (1 - sinE)(1 + sinE)

(1 - sinE) / (1 + sinE)

(cosec E -1)/(cosecE+1)