Question

10th-Maths-Trigonometry-

If cosecA+cotA=K,
Then prove that-cosA=K^2 - 1/K^2 + 1

Answer 1

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Answer 2

Step-by-step explanation:

given

$\cosec A+ cotA = k$

Now RHS

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

$= \frac{2cot A(cot A + cosec A)}{2cosec A(cosec A + cot A)} \\ \\ = \frac{cot A}{cosec a} \\ \\ = cos A$