Question

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TRIGONOMETRY CLASS 10

Answer 1

Hey refer to the attachment

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Answer 2

Answer:

To Prove: $\frac{cos\,A-sin\,A+1}{cos\,A+sin\,A-1}=cosec\,A+cot\,A$

Consider,

$LHS=\frac{cos\,A-sin\,A+1}{cos\,A+sin\,A-1}$

$=\frac{\frac{cos\,A}{sin\,A}-\frac{sin\,A}{sin\,A}+\frac{1}{sin\,A}}{\frac{cos\,A}+\frac{sin\,A}{sin\,A}-\frac{1}{sin\,A}}$

$=\frac{cot\,A-1+cosec\,A}{cot\,A+1-cosec\,A}$

$=\frac{cot\,A+cosec\,A-1}{1+cot\,A-cosec\,A}$

$=\frac{cot\,A+cosec\,A-(cosec^2\,A-cot^2\,A)}{1+cot\,A-cosec\,A}$

$=\frac{cot\,A+cosec\,A-(cosec\,A-cot\,A)(cosec\,A+cot\,A)}{1+cot\,A-cosec\,A}$

$=\frac{cot\,A+cosec\,A(1-(cosec\,A-cot\,A))}{1+cot\,A-cosec\,A}$

$=\frac{cot\,A+cosec\,A(1-cosec\,A+cot\,A)}{1+cot\,A-cosec\,A}$

$=cot\,A+cosec\,A$

$=RHS$

Hence Proved