Question

(V
)
cos A - sin A +1
= cosec A + cot A, using the identity cose
cos A + sin A-1​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{cos(A)-sin(A)+1}{cos(A)+sin(A)-1}}$

$\tt{=\dfrac{\dfrac{cos(A)-sin(A)+1}{sin(A)}}{\dfrac{cos(A)+sin(A)-1}{sin(A)}}}$

$\tt{=\dfrac{cot(A)-1+cosec(A)}{cot(A)+1-cosec(A)}}$

$\tt{=\dfrac{cot(A)+cosec(A)-1}{cot(A)-cosec(A)+1}}$

$\tt{=\dfrac{cot(A)+cosec(A)-\{cosec^2(A)-cot^2(A)\}}{cot(A)-cosec(A)+1}}$

$\tt{=\dfrac{cot(A)+cosec(A)-\{cosec(A)-cot(A)\}\{cosec(A)+cot(A)\}}{cot(A)-cosec(A)+1}}$

$\tt{=\dfrac{cot(A)+cosec(A)\{1-cosec(A)+cot(A)\}}{cot(A)-cosec(A)+1}}$

$\tt{=\dfrac{cot(A)+cosec(A)\{cot(A)-cosec(A)+1\}}{cot(A)-cosec(A)+1}}$

$\tt{=cosec(A)+cot(A)}$