Question

CosA-SinA+1 / CosA+SinA-1 =CosecA +CotA





Plzz sir/mam answer my question

Answer 1

Answer:

Step-by-step explanation:

LHS

[cos A - sin A + 1 ] / [ cos A + sin A - 1]

Divide each term in Numerator and Denominator by sin A

[(cos A / sin A) - ( sin A / sin A) + ( 1 / sin A)] / [(cos A / sin A) + ( sin A / sin A) - ( 1 / sin A)

[∵ cosФ/sinФ = cotФ, 1/sinФ = cosecФ]

∴ [cot A - 1 + cosec A] / [cot A + 1 - cosec A]  

Now we will change Numerator only, Denominator shall remain same

[ cosec A + cot A - ] / [ cot A + 1 - cosec A]

∵ cosec²Ф - cot²Ф = 1, we will put 1 = cosec²Ф - cot²Ф in Numerator

[cosec A + cot A - ( cosec²A - cot²A)]/ [ cot A + 1 - cosec A]

Applying a² - b² = ( a + b ) ( a - b)

[cosec A + cot A - ( cosec A + cot A)(cosec A - cotA)/[ cot A + 1 - cosec A]

Taking (cosec A + cot A) common from Numerator

(cosec A + cot A) [ 1 - (cosec A - cot A)] /[ cot A + 1 - cosec A]

(cosec A + cot A) (1 - cosec A + cot A)/ (cot A + 1 - cosec A)

[ cot A + 1 - cosec A] is cancelled from Numerator and Denominator

(cosec A + cot A) = RHS