1.

If a cot θ= b, the value of \(\frac{{a\sin \theta \; + \;b\cos \theta }}{{a\sin \theta - b\cos \theta }}\)1). \(\frac{{a - b}}{{{a^2}\; + \;{b^2}}}\)2). \(\frac{{a\; + \;b}}{{{a^2}\; + \;{b^2}}}\)3). \(\frac{{{a^2}\; + \;{b^2}}}{{{a^2} - {b^2}}}\)4). \(\frac{{{a^2} - {b^2}}}{{{a^2}\; + \;{b^2}}}\)

Answer»

a COT θ= b

tanθ = a/b

$(\frac{{a\SIN \theta \; + \;b\cos \theta }}{{a\sin \theta - b\cos \theta }} = \;\frac{{a(\sin \theta /cos\theta ) - b(\cos \theta /cos\theta )}}{{a(\sin \theta /cos\theta )\; + \;b(\cos \theta /cos\theta )}}\; = \frac{{a\tan \theta \; + \;b}}{{a\tan \theta - b}} = \frac{{a\; \times \;\LEFT( {\frac{a}{b}} \right)\; + \;b}}{{a\; \times \;\left( {\frac{a}{b}} \right) - b}} = \;\frac{{{a^2}\; + \;{b^2}}}{{{a^2} - {b^2}}})$


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