If theta = 3, alpha and sin, theta = frac{a}{ | vedclass

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Question

$a \,cosec\alpha - bsec\alpha $ $=$  $\frac{a}{{\sin \alpha }}\,\, - \,\,\frac{b}{{\cos \alpha }}$

$\frac{{\sqrt {{a^2} + {b^2}} }}{{\sin \alp

Vedclass · Accepted Answer

$2 \sqrt {{a^2}\,\, + \,\,{b^2}}$

Vedclass · Answer

$a \,cosec\alpha - bsec\alpha $ $=$  $\frac{a}{{\sin \alpha }}\,\, - \,\,\frac{b}{{\cos \alpha }}$

$\frac{{\sqrt {{a^2} + {b^2}} }}{{\sin \alpha \,\,\cos \alpha }}\,\,\,\left[ {\frac{a}{{\sqrt {{a^2} + {b^2}} }}\,\,\cos \alpha \, - \,\frac{b}{{\sqrt {{a^2} + {b^2}} }}\,\sin \alpha } \right]$

Now $sin3\alpha =$ $\frac{a}{{\sqrt {{a^2} + {b^2}} }}$ gives 

$ \Rightarrow \,\,\sqrt {{a^2} + {b^2}} \,\,\left[ {\frac{{\sin 3\alpha \,\cos \alpha \,\, - \,\,\cos 3\alpha \,\,\sin \alpha }}{{\sin \alpha \,\,\cos \alpha }}} \right] = 2\sqrt {{a^2}\, + \,{b^2}} $

If $\theta = 3\, \alpha$ and $sin\, \theta =$ $\frac{a}{{\sqrt {{a^2}\,\, + \,\,{b^2}} }}$. The value of the expression , $a \,cosec\, \alpha - b \,sec\, \alpha$ is

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